What is the derivative of (ln(x))^{4sin(x)} ?

The derivative of (ln(x))^{4sin(x)} is 4ln^{4sin(x)}(x)(cos(x)ln(ln(x))+(sin(x))/(xln(x)))

What is the first derivative of (ln(x))^{4sin(x)} ?

The first derivative of (ln(x))^{4sin(x)} is 4ln^{4sin(x)}(x)(cos(x)ln(ln(x))+(sin(x))/(xln(x)))

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derivative of

(ln (x))^{4 s i n (x)}

4 ln^{4 s i n (x)} (x) (cos (x) ln (ln (x)) + \frac{sin ( x )}{x ln ( x )})

Solution steps

\frac{d}{d x} ((ln (x))^{4 s i n (x)})

Apply exponent rule:

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

(ln (x))^{4 s i n (x)} = e^{4 s i n (x) l n (l n (x))}

= \frac{d}{d x} (e^{4 s i n (x) l n (l n (x))})

Apply the chain rule:

e^{4 s i n (x) l n (l n (x))} \frac{d}{d x} (4 sin (x) ln (ln (x)))

= e^{4 s i n (x) l n (l n (x))} \frac{d}{d x} (4 sin (x) ln (ln (x)))

\frac{d}{d x} (4 sin (x) ln (ln (x))) = 4 (cos (x) ln (ln (x)) + \frac{sin ( x )}{x ln ( x )})

= e^{4 s i n (x) l n (l n (x))} \cdot 4 (cos (x) ln (ln (x)) + \frac{sin ( x )}{x ln ( x )})

e^{4 s i n (x) l n (l n (x))} = ln^{4 s i n (x)} (x)

= 4 ln^{4 s i n (x)} (x) (cos (x) ln (ln (x)) + \frac{sin ( x )}{x ln ( x )})

\int (4 - 4 x)^{7} d x

n = 1 \sum \infty - (\frac{2}{3})^{n - 1}

\frac{d}{d θ} (cot^{2} (sin (θ)))

5 (ln (y)) y^{^{'}} - x^{3} y = 0

\int 8 tan (x) sec^{4} (x) d x

What is the derivative of (ln(x))^{4sin(x)} ?
The derivative of (ln(x))^{4sin(x)} is 4ln^{4sin(x)}(x)(cos(x)ln(ln(x))+(sin(x))/(xln(x)))
What is the first derivative of (ln(x))^{4sin(x)} ?
The first derivative of (ln(x))^{4sin(x)} is 4ln^{4sin(x)}(x)(cos(x)ln(ln(x))+(sin(x))/(xln(x)))