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study help
mathematics
precalculus
Questions and Answers of
Precalculus
What is the difference between the (Simple) Power Rule and the General Power Rule?
Explain when you have to use implicit differentiation to find a derivative.
Estimate the slope of the graph at the points (x1, y1) and (x2, y2). pougos d A omb y mms 빼 (X32) X
Use the graph shown in the figure. To print an enlarged copy of the graph, go to MathGraphs.com.Insert the proper inequality symbol (< or >) between the given quantities. (a) (b)
Describe the relationship between continuity and differentiability.
What is a higher-order derivative?
Describe the difference between average velocity and velocity.
Find dy/dx by implicit differentiation.x2 − y2 = 25
Find dy/dx by implicit differentiation.x5 + y5 = 16
Use the Product Rule to find the derivative of the function.g(s) = √s(s2 + 8)
Find dy/dx by implicit differentiation.2x3 + 3y3 = 64
Find the derivative of the function.y = (2x − 7)3
Use the rules of differentiation to find the derivative of the function.y = x7
Use the Quotient Rule to find the derivative of the function. g(t) || 31²2 1 - 2t + 5
Find the derivative of the function.y = 5(2 − x3)4
Use the Product Rule to find the derivative of the function.g(x) = √x sin x
Find dy/dx by implicit differentiation.x2 y + y2 x = −2
Find the derivative of the function.g(x) = 3(4 − 9x)5/6
Find dy/dx by implicit differentiation.x3 y3 − y = x
Find the slope of the tangent line to the graph of the function at the given point.f(x) = 5 − x2, (3, −4)
Find dy/dx by implicit differentiation.√xy = x2 y + 1
Use the Quotient Rule to find the derivative of the function. f(t) = COS t 1³
Find the derivative of the function.h(s) = −2√5s2 + 3
Find dy/dx by implicit differentiation.x3 − 3x2 y + 2xy2 = 12
Find the derivative of the function.g(x) = √4 − 3x2
Find dy/dx by implicit differentiation.x4y − 8xy + 3xy2 = 9
Find the derivative of the function.y = 3√6x2 + 1
Find the derivative of the function.y = 2 4√9 − x2
Find dy/dx by implicit differentiation.(sin x + cos y)2 = 2
Find the derivative of the function.y = 1/x − 2
Find dy/dx by implicit differentiation.csc x = x(1 + tan y)
Find the derivative of the function.s(t) = 1/ 4 − 5t − t2
Find the derivative of the function.g(s) = 6/ (s3 − 2)3
Find dy/dx by implicit differentiation.y = sin xy
Find the derivative of the function.g(t) = 1/ √t2 − 2
Find the derivative of the function by the limit process.f(x) = x2 − 5
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. 1² || x² - 49 x² + 49' (7,0)
Find the derivative of the function.f(x) = x2 (x − 2)7
Find the derivative of the function by the limit process.g(t) = t3 + 4t
Find the derivative of the function by the limit process. x (x) f
Use the rules of differentiation to find the derivative of the function.g(t) = cos t
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.xy = 6, (−6, −1)
Find the derivative of the function.y = x√1 − x2
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.3x3 y = 6, (1, 2)
Find the derivative of the function.y = x2 √16 − x2
Use the rules of differentiation to find the derivative of the function.y = 7x4 + 2 sin x
Complete the table to find the derivative of the function. Original Function Rewrite Differentiate Simplify 3 (2x)-2 y
Find the derivative of the function.y = x/ √x2 + 1
Find the derivative of the function by the limit process.h(s) = −2√s
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. x cos y = 1, (2₁3)
Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.(x + y)3 = x3 + y3, (−1, 1)
Find the derivative of the function.g(x) = (x + 5/ x2 + 2)2
Find the derivative of the function.h(t) = (t2 / t3 + 2)2
Find the derivative of the function.s(t) = (1 + t / t + 3)4
Find the derivative of the function.g(x) = (3x2 − 2 / 2x + 3)−2
Find the derivative of the trigonometric function.f(t) = 3 sec (πt − 1)2
Find the derivative of the trigonometric function. h(x) || 1 X 12 sec x
Find the derivative of the function.f(t) = t2/3 − t1/3 + 4
Find the derivative of the trigonometric function. y || sec x X
Find the derivative of the trigonometric function.y = 5 cos(πx)2
Find the derivative of the algebraic function. f(x) = x¹(1 2 x + 1)
Find the slope of the tangent line to the graph at the given point. Bifolium: (x² + y²)² = 4x²y y -2 2 - 1 -2- (1, 1) + 12 X
Find the slope of the tangent line to the graph at the given point. Cissoid: (4- x)² = x³ y 2 1 -1 -2 (2, 2) 2 3 نیا X
Find the derivative of the algebraic function. h(x) = + 5x x + 1
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Parabola 10 ∞642 8 y -2 -4 -6 + (y - 3)² = 4(x - 5) (6,
Find the slope of the tangent line to the graph at the given point. Folium of Descartes: ³+3³6xy = 0 y 4 3 2 1 نیا -2. TIM w 100 12 3 4
Find the derivative of the function.f(x) = ((x2 + 3)5 + x)2
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Circle (x + 2)² + (y - 3)² = 37 y 10 ∞642 8 -4-2 -4+ (4,4) +1
Find the derivative of the algebraic function.f(x) = 3√ x(√x + 3)
Find the derivative of the trigonometric function.y = cos 4x
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Cruciform x²y²-9x²-4y² = 0 y 4 (-4, 2√3)- H -6-4-2 J X H
Find the derivative of the trigonometric function.y = sin x
Find the derivative of the algebraic function. g(x) = 2 IN X 1 1 x + 1
Find the derivative of the trigonometric function.g(x) = 5 tan 3x
Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.Function
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Astroid 12 y -12 + x-2/3 + y2/3 = 5 (8, 1) 12
Find the derivative of the trigonometric function.h(x) = sec 6x
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Kappa curve |y²(x² + y²) = 2x² y -3-2 3 2 نیا (1,
Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.Function
Find an equation of the line that is tangent to the graph of f and parallel to the given line.Function Linef(x) = 2x2
Find an equation of the tangent line to the graph at the given point. To print an enlarged copy of the graph, go to MathGraphs.com. Lemniscate 3(x² + y²)² = 100(x² -
Find the derivative of the trigonometric function.y = sin(x)2
Find the derivative of the trigonometric function.y = csc(1 − 2x)2
Find the derivative of the algebraic function.f(x) = (x3 − x)(x2 + 2)(x2 + x − 1)
Find the derivative of the function.f(x) = x3 − 2x + 3x−3
Find the derivative of the trigonometric function. f(x) = sin x x3
Sketch the graph of f′. Explain how you found your answer. 7 432 1 y +x X 1 2 3 4 5 6 7 8
Find the derivative of the trigonometric function.g(θ) = sec(1/2 θ) tan(1/2 θ)
Find the derivative of the trigonometric function.f(θ) = (θ + 1) cos θ
Write two different equations in implicit form that you can write in explicit form. Then write two different equations in implicit form that you cannot write in explicit form.
Find the derivative of the trigonometric function.f(x) = cot x / sin x
Explain why the derivative of x2 + y2 + 2 = 1 does not mean anything.
Find the derivative of the trigonometric function.y = 4 sec2 x
Find the derivative of the trigonometric function.g(t) = 5 cos2 t
Find the derivative of the trigonometric function.y = x + cot x
Find the derivative of the function.y = x(x2 + 1)
Find the derivative of the trigonometric function.h(t) = 2 cot2 (πt + 2)
Find the derivative of the function.f(x) = x2 + 5 − 3x−2
The limit represents f′(c) for a function f and a number c. Find f and c. lim Δr - 0 (-2 + Δx) + 8 Δε
Sketch a graph of a function whose derivative is zero at exactly two points. Explain how you found the answer.
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