What is the derivative of sin^{ln(x}(9x)) ?

The derivative of sin^{ln(x}(9x)) is x^{ln(sin(9x))}((ln(sin(9x)))/x+9cot(9x)ln(x))

What is the first derivative of sin^{ln(x}(9x)) ?

The first derivative of sin^{ln(x}(9x)) is x^{ln(sin(9x))}((ln(sin(9x)))/x+9cot(9x)ln(x))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (sin^{l n (x)} (9 x))

x^{l n (s i n (9 x))} (\frac{ln ( sin ( 9 x ) )}{x} + 9 cot (9 x) ln (x))

Solution steps

\frac{d}{d x} (sin^{l n (x)} (9 x))

Apply exponent rule:

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

sin^{l n (x)} (9 x) = e^{l n (x) l n (s i n (9 x))}

= \frac{d}{d x} (e^{l n (x) l n (s i n (9 x))})

Apply the chain rule:

e^{l n (x) l n (s i n (9 x))} \frac{d}{d x} (ln (x) ln (sin (9 x)))

= e^{l n (x) l n (s i n (9 x))} \frac{d}{d x} (ln (x) ln (sin (9 x)))

\frac{d}{d x} (ln (x) ln (sin (9 x))) = \frac{ln ( sin ( 9 x ) )}{x} + 9 cot (9 x) ln (x)

= e^{l n (x) l n (s i n (9 x))} (\frac{ln ( sin ( 9 x ) )}{x} + 9 cot (9 x) ln (x))

e^{l n (x) l n (s i n (9 x))} = x^{l n (s i n (9 x))}

= x^{l n (s i n (9 x))} (\frac{ln ( sin ( 9 x ) )}{x} + 9 cot (9 x) ln (x))

arccsc (- 4 t^{2})

\frac{\partial}{\partial x} (5 x (3 + y)^{- 1})

\frac{d ^{2}}{d x ^{2}} (7 cos (3 x))

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

What is the derivative of sin^{ln(x}(9x)) ?
The derivative of sin^{ln(x}(9x)) is x^{ln(sin(9x))}((ln(sin(9x)))/x+9cot(9x)ln(x))
What is the first derivative of sin^{ln(x}(9x)) ?
The first derivative of sin^{ln(x}(9x)) is x^{ln(sin(9x))}((ln(sin(9x)))/x+9cot(9x)ln(x))