Chain Rule and Implicit Differentiation

Practice Questions

AP Calculus BC › Chain Rule and Implicit Differentiation

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1

$g(x) = e ^{x^{2}+x}$

Evaluate .

2

Use implicit differentiation to find the slope of the tangent line to $\small y^3-lny=x^2$ at the point $\small (1,1)$ .

3

$g (x) = \frac{1}{4x - 7}$

Evaluate .

4

Screen shot 2016 03 31 at 11.11.35 am

Figure. Squircle of "radius" 1

A squircle is a curve in the xy plane that appears like a rounded square, but whose points satisfy the following equation (analogous to the Pythagorean theorem for a circle)

where the constant is the "radius" of the squircle.

Using implicit differentiation, obtain an expression for $\frac{dy}{dx}$ as a function of both and .

5

A curve in the xy plane is given implictly by

.

Calculate the slope of the line tangent to the curve at the point .

6

Find $\frac{\mathrm{d} \delta}{\mathrm{d} x}$ from the following equation:

$5=\delta e^{x^2}$ , where $\delta$ is a function of x.

7

Find :

$f=\gamma \cos(x^2)$ , where $\gamma$ is a constant.

8

Find the first derivative of the following function:

$f=\sec(x^2)+\ln(2x^2)$

9

Find dx/dy by implicit differentiation:

$x^3+x\tan^{-1}(y)=e^y$

10

Given the relation , find $\frac{dy}{dx}$ .

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