(a) Using the first principle of differentiation, determine the derivative of f(x) = 2x-3x+5 at z...

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(a) Using the first principle of differentiation, determine the derivative of f(x) = 2x²-3x+5 at z = 2. (b) Find the derivatives of the following functions by using the appropriate rules for differentiation: (i) h(r) = (r²-ar)(√ar²+1), a 20 (ii) y(t) = tan √cos (8t) (iii) g(x) = (c) Use the Fundamental Theorem of Calculus to find the derivative of costanz r> 0. raine K(x) = (5+1²) dt Joosz (d) Given y cos(2x) = zsin(2y) find (i) using implicit differentiation. dy dr (ii) the equation of the tangent line to the curve y cos(2x) = zsin(2y) at the point (.). (5) (3) (3) (3) (3) > : (a) Using the first principle of differentiation, determine the derivative of f(x) = 2x²-3x+5 at z = 2. (b) Find the derivatives of the following functions by using the appropriate rules for differentiation: (i) h(r) = (r²-ar)(√ar²+1), a 20 (ii) y(t) = tan √cos (8t) (iii) g(x) = (c) Use the Fundamental Theorem of Calculus to find the derivative of costanz r> 0. raine K(x) = (5+1²) dt Joosz (d) Given y cos(2x) = zsin(2y) find (i) using implicit differentiation. dy dr (ii) the equation of the tangent line to the curve y cos(2x) = zsin(2y) at the point (.). (5) (3) (3) (3) (3) > :

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a To find the derivative of the function fx 2x2 3x 5 we apply the power rule and the constant rule The derivative of 2x2 is 4x the derivative of 3x is 3 and the derivative of 5 is 0 Therefore the deri... View the full answer