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Popular >

derivative of ln(xsqrt(x^2+7))

Solution

derivative of

ln (x x^{2} + 7)

Solution

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

Solution steps

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

Apply the chain rule:

\frac{1}{x x ^{2} + 7} \frac{d}{d x} (x x^{2} + 7)

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

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

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

Simplify

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

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

Popular Examples

integral of ((cos(x)))/(sin(x))

\int \frac{( cos ( x ) )}{sin ( x )} d x

derivative of 1/t derivative of

\frac{1}{t}

derivative of sqrt((x+1/(x-1)))

\frac{d}{d x} (\frac{x + 1}{x - 1})

limit as x approaches 0+of 1+1/x

x \to 0 + lim (1 + \frac{1}{x})

laplacetransform 5e^{-2(t-1)}laplace transform

5 e^{- 2 (t - 1)}

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2+7)) ?
The derivative of ln(xsqrt(x^2+7)) is (2x^2+7)/(x(x^2+7))
What is the first derivative of ln(xsqrt(x^2+7)) ?
The first derivative of ln(xsqrt(x^2+7)) is (2x^2+7)/(x(x^2+7))