What is the derivative of (10x^{ln(10x)}) ?

The derivative of (10x^{ln(10x)}) is (2e^{ln^2(10x)}ln(10x))/x

What is the first derivative of (10x^{ln(10x)}) ?

The first derivative of (10x^{ln(10x)}) is (2e^{ln^2(10x)}ln(10x))/x

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\frac{d}{d x} ((10 x)^{l n (10 x)})

\frac{2 e ^{l n^{2} (10 x)} ln ( 10 x )}{x}

Solution steps

\frac{d}{d x} ((10 x)^{l n (10 x)})

Apply exponent rule:

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

(10 x)^{l n (10 x)} = e^{l n (10 x) l n (10 x)}

= \frac{d}{d x} (e^{l n (10 x) l n (10 x)})

Apply the chain rule:

e^{l n (10 x) l n (10 x)} \frac{d}{d x} (ln (10 x) ln (10 x))

= e^{l n (10 x) l n (10 x)} \frac{d}{d x} (ln (10 x) ln (10 x))

\frac{d}{d x} (ln (10 x) ln (10 x)) = \frac{2 ln ( 10 x )}{x}

= e^{l n (10 x) l n (10 x)} \frac{2 ln ( 10 x )}{x}

Simplify

e^{l n (10 x) l n (10 x)} \frac{2 ln ( 10 x )}{x} : \frac{2 e ^{l n^{2} (10 x)} ln ( 10 x )}{x}

= \frac{2 e ^{l n^{2} (10 x)} ln ( 10 x )}{x}

\frac{\partial}{\partial x} (tan (x - y))

\int ln (1) d x

(x^{3} + e^{y}) d y = 3 x^{2} d x

y^{^{'}} + 8 y = x e^{- 8 x}

64 - x^{2}

What is the derivative of (10x^{ln(10x)}) ?
The derivative of (10x^{ln(10x)}) is (2e^{ln^2(10x)}ln(10x))/x
What is the first derivative of (10x^{ln(10x)}) ?
The first derivative of (10x^{ln(10x)}) is (2e^{ln^2(10x)}ln(10x))/x