What is the derivative of (x^2+4/(x+5)) ?

The derivative of (x^2+4/(x+5)) is (x^2+10x-4)/((x+5)^2)

What is the first derivative of (x^2+4/(x+5)) ?

The first derivative of (x^2+4/(x+5)) is (x^2+10x-4)/((x+5)^2)

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\frac{d}{d x} (\frac{x ^{2} + 4}{x + 5})

\frac{x ^{2} + 10 x - 4}{( x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 4}{x + 5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 4 ) ( x + 5 ) - \frac{d}{d x} ( x + 5 ) ( x ^{2} + 4 )}{( x + 5 ) ^{2}}

\frac{d}{d x} (x^{2} + 4) = 2 x

\frac{d}{d x} (x + 5) = 1

= \frac{2 x ( x + 5 ) - 1 \cdot ( x ^{2} + 4 )}{( x + 5 ) ^{2}}

Simplify

\frac{2 x ( x + 5 ) - 1 \cdot ( x ^{2} + 4 )}{( x + 5 ) ^{2}} : \frac{x ^{2} + 10 x - 4}{( x + 5 ) ^{2}}

= \frac{x ^{2} + 10 x - 4}{( x + 5 ) ^{2}}

\int_{1}^{e^{4}} \frac{ln ^{2} ( x ^{2} )}{x} d x

\int_{- 1}^{2} x^{3} d x

x \to \infty lim (0. 6^{x})

f (x) = ln (x)

\frac{d}{d x} ((x + (x + sin^{2} (x))^{7})^{3})

What is the derivative of (x^2+4/(x+5)) ?
The derivative of (x^2+4/(x+5)) is (x^2+10x-4)/((x+5)^2)
What is the first derivative of (x^2+4/(x+5)) ?
The first derivative of (x^2+4/(x+5)) is (x^2+10x-4)/((x+5)^2)