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Popular >

derivative of ln(x^2+5x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

Popular Examples

integral from 0 to 1 of 1/(sqrt(3-2x))

\int_{0}^{1} \frac{1}{3 - 2 x} d x

tangent of f(x)=x^2,\at x=4 tangent of

f (x) = x^{2}, at x = 4

derivative of 2+3e^{-3/x}

\frac{d}{d x} (2 + 3 e^{- \frac{3}{x}})

derivative of (x^4+3x^2-5^4)

\frac{d}{d x} ((x^{4} + 3 x^{2} - 5)^{4})

derivative of 3xe^{5x}

\frac{d}{d x} (3 x e^{5 x})

Frequently Asked Questions (FAQ)

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