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

The derivative of sin(x^{ln(x})) is (2e^{ln^2(x)}ln(x)cos(x^{ln(x)}))/x

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

The first derivative of sin(x^{ln(x})) is (2e^{ln^2(x)}ln(x)cos(x^{ln(x)}))/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 (x^{l n (x)}))

\frac{2 e ^{l n^{2} (x)} ln ( x ) cos ( x ^{l n (x)} )}{x}

Solution steps

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

Apply the chain rule:

cos (x^{l n (x)}) \frac{d}{d x} (x^{l n (x)})

= cos (x^{l n (x)}) \frac{d}{d x} (x^{l n (x)})

\frac{d}{d x} (x^{l n (x)}) = \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

= cos (x^{l n (x)}) \frac{2 e ^{l n^{2} (x)} ln ( x )}{x}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 e ^{l n^{2} (x)} ln ( x ) cos ( x ^{l n (x)} )}{x}

y = 4 9 - x^{2}

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

f (x) = 9 - 16 x

\int (8 x^{7} + 9) x^{8} + 9 x d x

y = \frac{8}{x ^{2}}

What is the derivative of sin(x^{ln(x})) ?
The derivative of sin(x^{ln(x})) is (2e^{ln^2(x)}ln(x)cos(x^{ln(x)}))/x
What is the first derivative of sin(x^{ln(x})) ?
The first derivative of sin(x^{ln(x})) is (2e^{ln^2(x)}ln(x)cos(x^{ln(x)}))/x