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

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

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

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

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\frac{d}{d x} ((ln (x))^{c o s (4 x)})

ln^{c o s (4 x)} (x) (- 4 sin (4 x) ln (ln (x)) + \frac{cos ( 4 x )}{x ln ( x )})

Solution steps

\frac{d}{d x} ((ln (x))^{c o s (4 x)})

Apply exponent rule:

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

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

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

Apply the chain rule:

e^{c o s (4 x) l n (l n (x))} \frac{d}{d x} (cos (4 x) ln (ln (x)))

= e^{c o s (4 x) l n (l n (x))} \frac{d}{d x} (cos (4 x) ln (ln (x)))

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

= e^{c o s (4 x) l n (l n (x))} (- 4 sin (4 x) ln (ln (x)) + \frac{cos ( 4 x )}{x ln ( x )})

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

= ln^{c o s (4 x)} (x) (- 4 sin (4 x) ln (ln (x)) + \frac{cos ( 4 x )}{x ln ( x )})

\frac{x ^{2}}{12}

x \to + 3 - lim (sin (π + x) + 1)

y = 20 - x^{2} and y = 2 x + 5, - 2 \leq x \leq 8

\int \frac{22}{( 121 x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial x} (x yz - cos (x + y + z))

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