What is the derivative of (ln(x)^{sinh(x)}) ?

The derivative of (ln(x)^{sinh(x)}) is ln^{sinh(x)}(x)(cosh(x)ln(ln(x))+(sinh(x))/(xln(x)))

What is the first derivative of (ln(x)^{sinh(x)}) ?

The first derivative of (ln(x)^{sinh(x)}) is ln^{sinh(x)}(x)(cosh(x)ln(ln(x))+(sinh(x))/(xln(x)))

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\frac{d}{d x} ((ln (x))^{s i n h (x)})

ln^{s i n h (x)} (x) (cosh (x) ln (ln (x)) + \frac{sinh ( x )}{x ln ( x )})

Solution steps

\frac{d}{d x} ((ln (x))^{s i n h (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

(ln (x))^{s i n h (x)} = e^{s i n h (x) l n (l n (x))}

= \frac{d}{d x} (e^{s i n h (x) l n (l n (x))})

Apply the chain rule:

e^{s i n h (x) l n (l n (x))} \frac{d}{d x} (sinh (x) ln (ln (x)))

= e^{s i n h (x) l n (l n (x))} \frac{d}{d x} (sinh (x) ln (ln (x)))

\frac{d}{d x} (sinh (x) ln (ln (x))) = cosh (x) ln (ln (x)) + \frac{sinh ( x )}{x ln ( x )}

= e^{s i n h (x) l n (l n (x))} (cosh (x) ln (ln (x)) + \frac{sinh ( x )}{x ln ( x )})

e^{s i n h (x) l n (l n (x))} = ln^{s i n h (x)} (x)

= ln^{s i n h (x)} (x) (cosh (x) ln (ln (x)) + \frac{sinh ( x )}{x ln ( x )})

\int 9 cos (x) sin (x) d x

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

f (x) = 2 x^{3} - 4 x^{2}, at x = 1

\int_{1}^{5} \frac{5}{x ^{2} + 4 x + 4} d x

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

What is the derivative of (ln(x)^{sinh(x)}) ?
The derivative of (ln(x)^{sinh(x)}) is ln^{sinh(x)}(x)(cosh(x)ln(ln(x))+(sinh(x))/(xln(x)))
What is the first derivative of (ln(x)^{sinh(x)}) ?
The first derivative of (ln(x)^{sinh(x)}) is ln^{sinh(x)}(x)(cosh(x)ln(ln(x))+(sinh(x))/(xln(x)))