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Popular >

derivative of f(x)=(x^2)/(x+7)

Solution

derivative of

f (x) = \frac{x ^{2}}{x + 7}

Solution

\frac{x ^{2} + 14 x}{( x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x + 7})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} ) ( x + 7 ) - \frac{d}{d x} ( x + 7 ) x ^{2}}{( x + 7 ) ^{2}}

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (x + 7) = 1

= \frac{2 x ( x + 7 ) - 1 \cdot x ^{2}}{( x + 7 ) ^{2}}

Simplify

\frac{2 x ( x + 7 ) - 1 \cdot x ^{2}}{( x + 7 ) ^{2}} : \frac{x ^{2} + 14 x}{( x + 7 ) ^{2}}

= \frac{x ^{2} + 14 x}{( x + 7 ) ^{2}}

Popular Examples

f(x)=(3x^2)/(ln(x))

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

integral of (x^3)/((6-x^4)^2)

\int \frac{x ^{3}}{( 6 - x ^{4} ) ^{2}} d x

integral of (7x^2+16x-19)/(x^2+2x-3)

\int \frac{7 x ^{2} + 16 x - 19}{x ^{2} + 2 x - 3} d x

derivative of f(x)= 1/(3(x)^2+2(x))derivative of

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

tangent of f(x)=2x^3+42x^2+288x+14 tangent of

f (x) = 2 x^{3} + 42 x^{2} + 288 x + 14

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(x+7) ?
The derivative of f(x)=(x^2)/(x+7) is (x^2+14x)/((x+7)^2)
What is the first derivative of f(x)=(x^2)/(x+7) ?
The first derivative of f(x)=(x^2)/(x+7) is (x^2+14x)/((x+7)^2)