question

Use implicit differentiation to find an equation for the tangent line to the curve at the given pointP.

cos(xy) +y=x⁴,P(1, 0)

and

A pointP(x,y)

moves along the graph of the equationy=x³+x²+7.

Thex-valuesare changing at the rate of2unitsper second. How fast are they-valueschanging (in units per second) at the pointQ(1,9)?

units/sec

and

Give your answer accurate to 3 decimal places.

The area of an equilateral triangle is decreasing at a rate of5cm²/min.Find the rate (in centimeters per minute) at which the length of a side is decreasing when the area of the triangle is300cm².

cm/min