What is the derivative of cosh(ln(e^{x^3})) ?

The derivative of cosh(ln(e^{x^3})) is sinh(x^3)*3x^2

What is the first derivative of cosh(ln(e^{x^3})) ?

The first derivative of cosh(ln(e^{x^3})) is sinh(x^3)*3x^2

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\frac{d}{d x} (cosh (ln (e^{x^{3}})))

sinh (x^{3}) \cdot 3 x^{2}

Solution steps

\frac{d}{d x} (cosh (ln (e^{x^{3}})))

Simplify

cosh (ln (e^{x^{3}})) : cosh (x^{3})

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

Apply the chain rule:

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

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

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

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

\int \frac{9}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

\int \frac{9}{x} d x

x^{2} d y = (5 y^{3} - 2 x y) d x

\int 4 x - 1 d x

\frac{d}{d x} ((x^{2} + 1)^{s i n (x)})

What is the derivative of cosh(ln(e^{x^3})) ?
The derivative of cosh(ln(e^{x^3})) is sinh(x^3)*3x^2
What is the first derivative of cosh(ln(e^{x^3})) ?
The first derivative of cosh(ln(e^{x^3})) is sinh(x^3)*3x^2