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Popular >

derivative of ln(sqrt(x^8+19))

Solution

\frac{d}{d x} (ln (x^{8} + 19))

Solution

\frac{4 x ^{7}}{x ^{8} + 19}

Solution steps

\frac{d}{d x} (ln (x^{8} + 19))

Apply the chain rule:

\frac{1}{x ^{8} + 19} \frac{d}{d x} (x^{8} + 19)

= \frac{1}{x ^{8} + 19} \frac{d}{d x} (x^{8} + 19)

\frac{d}{d x} (x^{8} + 19) = \frac{4 x ^{7}}{x ^{8} + 19}

= \frac{1}{x ^{8} + 19} \cdot \frac{4 x ^{7}}{x ^{8} + 19}

Simplify

\frac{1}{x ^{8} + 19} \cdot \frac{4 x ^{7}}{x ^{8} + 19} : \frac{4 x ^{7}}{x ^{8} + 19}

= \frac{4 x ^{7}}{x ^{8} + 19}

Popular Examples

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

\frac{d}{d t} (t^{3})

tangent of f(x)=x^2+3x+1,(-1,-1)tangent of

f (x) = x^{2} + 3 x + 1, (- 1, - 1)

integral of 2/((x+1)^3)

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

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(sqrt(x^8+19)) ?
The derivative of ln(sqrt(x^8+19)) is (4x^7)/(x^8+19)
What is the first derivative of ln(sqrt(x^8+19)) ?
The first derivative of ln(sqrt(x^8+19)) is (4x^7)/(x^8+19)