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Popular >

derivative of ln(sinh(x^3))

Solution

\frac{d}{d x} (ln (sinh (x^{3})))

Solution

3 x^{2} coth (x^{3})

Solution steps

\frac{d}{d x} (ln (sinh (x^{3})))

Apply the chain rule:

\frac{1}{sinh ( x ^{3} )} \frac{d}{d x} (sinh (x^{3}))

= \frac{1}{sinh ( x ^{3} )} \frac{d}{d x} (sinh (x^{3}))

\frac{d}{d x} (sinh (x^{3})) = cosh (x^{3}) \cdot 3 x^{2}

= \frac{1}{sinh ( x ^{3} )} cosh (x^{3}) \cdot 3 x^{2}

Simplify

\frac{1}{sinh ( x ^{3} )} cosh (x^{3}) \cdot 3 x^{2} : 3 x^{2} coth (x^{3})

= 3 x^{2} coth (x^{3})

Graph

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\int x^{5} cos (1 - x^{6}) d x

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\frac{s + 1}{s ^{2} + 4 s}

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x \to 0 lim (5 x - 3)

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f (x) = x^{2} + 3

Frequently Asked Questions (FAQ)

What is the derivative of ln(sinh(x^3)) ?
The derivative of ln(sinh(x^3)) is 3x^2coth(x^3)
What is the first derivative of ln(sinh(x^3)) ?
The first derivative of ln(sinh(x^3)) is 3x^2coth(x^3)