Free Printable 6.3 Implicit Differentiation Review

1.

Select all of the following that are implicitly defined functions.

a)

$4xy^{2\ }+3xy-4=12x$

b)

$y=2x^{3\ }-3x+1$

c)

$\sqrt{x}+2xy=y^3$

d)

$y=\sqrt{x+3}-11$

e)

$2xy^2-2x^2y=100$

2.

Find $\frac{dy}{dx}$ for the function $5x^3=-5y^3+3$

a)

$\frac{-15x^2}{-5y^3+3}$

b)

$-\frac{x^2}{y^2}$

c)

$-\frac{y^2}{x^2}$

d)

$\frac{5x^3}{-5y^3+3}$

3.

Find $\frac{dy}{dx}$ for the function $-5y^3-4x^2y+3=3x^2$

a)

$\frac{-5y^3-4x^2y+3}{3x^2}$

b)

$\frac{6x+8xy}{-15y^2-4x^2}$

c)

$\frac{6+8y}{3x}$

d)

$\frac{-15y^2-4x^2}{6x+8xy}$

4.

Find $\frac{d^2y}{dx^2}$ in terms of x and y for $2y^2+1=5x$

a)

$-\frac{25}{16y^3}$

b)

$\frac{8y^3-10y^2+4y-5}{25x^2}$

c)

$\frac{16y}{25}$

d)

$-\frac{1}{x^2}$

5.

What is the slope of the tangent line to $x=-2y^2+4$ at the point $\left(2,\ 1\right)$ ?

(Type your answer with NO spaces!)

(a)

6.

Write the equation of the tangent line to $4x-4y=4x^3y$ at the point $\left(0,\ 0\right)$

(a)

7.

Find the value of $\frac{dy}{dx}$ for the function $-2x^2+3=2x^3+3y^3$ at $x=-1$

a)

$-\frac{9}{2}$

b)

$2$

c)

$1$

d)

$-\frac{2}{9}$

8.

State the slope of the normal line to $\left(x-1\right)^2+\left(y-1\right)^2=13$
at the point $\left(3,\ 4\right)$

(Type your answer with NO spaces!)

(a)

9.

Write the equation of the normal line to the curve $y^4-x^4-y^2+x^2=0$ at the point $\left(1,\ 1\right)$

(Type your answer with NO spaces!)

(a)

10.

Find $\frac{d^2y}{dx^2}$ for $x=\cos\ y$

a)

$-\csc^2y\cot y$

b)

$-\csc y\cot y$

c)

$-\cot^2y$

d)

$-\sin x\sin y$

6.3 Implicit Differentiation Review

Total questions: 10

Worksheet time: 5mins

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