User:Melikamp/b-calc

< User:Melikamp

Differentiation Review

1. Write the product function

f(x)

and its rate of change function for

g(x)=2e^{5}x

and

h(x)=2x^{2}-x

.

f(x)=2e^{5}x(2x^{2}-x),\ f'(x)=2e^{5}(2x^{2}-x)+2e^{5}x(4x-1)

f(x)=2e^{5}x(2x^{2}-x),\ f'(x)=2e^{5}(2x^{2}-x)+2e^{5}x(4x-1)

2. Write the product function

f(x)

and its rate of change function for

g(x)=0.5\cos(4x)

and

h(x)=2\ln(x)

.

f(x)=\cos(4x)\ln(x),\ f'(x)=-4\sin(4x)\ln(x)+{\frac {\cos(4x)}{x}}

f(x)=\cos(4x)\ln(x),\ f'(x)=-4\sin(4x)\ln(x)+{\frac {\cos(4x)}{x}}

3. Find

f'(x)

if

f(x)=(2x+3)e^{-x}

.

2e^{-x}-(2x+3)e^{-x}

2e^{-x}-(2x+3)e^{-x}

4. Find

f'(x)

if

f(x)=2{\sqrt {x^{3}}}\ln(x)

.

3{\sqrt {x}}\ln(x)+2{\sqrt {x}}

3{\sqrt {x}}\ln(x)+2{\sqrt {x}}

5. Find

f'(x)

if

f(x)=(x+2)^{3}(1-x^{2})

.

3(x+2)^{2}(1-x^{2})-2x(x+2)^{3}

3(x+2)^{2}(1-x^{2})-2x(x+2)^{3}

6. Find

f'(x)

if

\displaystyle f(x)={\frac {e^{x}}{x}}

.

\displaystyle {\frac {xe^{x}-e^{x}}{x^{2}}}

\displaystyle {\frac {xe^{x}-e^{x}}{x^{2}}}

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