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Popular >

derivative of sqrt(x^2+5x)

Solution

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

Solution

\frac{2 x + 5}{2 x ^{2} + 5 x}

Solution steps

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

Apply the chain rule:

\frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

= \frac{1}{2 x ^{2} + 5 x} \frac{d}{d x} (x^{2} + 5 x)

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

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

Simplify

\frac{1}{2 x ^{2} + 5 x} (2 x + 5) : \frac{2 x + 5}{2 x ^{2} + 5 x}

= \frac{2 x + 5}{2 x ^{2} + 5 x}

Popular Examples

integral from 0 to pi of sin(x/2)

\int_{0}^{π} sin (\frac{x}{2}) d x

integral of (1+sqrt(x^2+1))/((x^2+1)^{3/2)}

\int \frac{1 + x ^{2} + 1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

integral of 17xe^{-x^2}

\int 17 x e^{- x^{2}} d x

(dy)/(dx)=(cos(13x))/(e^{13y)}

\frac{d y}{d x} = \frac{cos ( 13 x )}{e ^{13 y}}

integral of 7^{-2x}

\int 7^{- 2 x} d x

Frequently Asked Questions (FAQ)

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