What is the derivative of (7x^{ln(7x)}) ?

The derivative of (7x^{ln(7x)}) is (2e^{ln^2(7x)}ln(7x))/x

What is the first derivative of (7x^{ln(7x)}) ?

The first derivative of (7x^{ln(7x)}) is (2e^{ln^2(7x)}ln(7x))/x

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\frac{d}{d x} ((7 x)^{l n (7 x)})

\frac{2 e ^{l n^{2} (7 x)} ln ( 7 x )}{x}

Solution steps

\frac{d}{d x} ((7 x)^{l n (7 x)})

Apply exponent rule:

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

(7 x)^{l n (7 x)} = e^{l n (7 x) l n (7 x)}

= \frac{d}{d x} (e^{l n (7 x) l n (7 x)})

Apply the chain rule:

e^{l n (7 x) l n (7 x)} \frac{d}{d x} (ln (7 x) ln (7 x))

= e^{l n (7 x) l n (7 x)} \frac{d}{d x} (ln (7 x) ln (7 x))

\frac{d}{d x} (ln (7 x) ln (7 x)) = \frac{2 ln ( 7 x )}{x}

= e^{l n (7 x) l n (7 x)} \frac{2 ln ( 7 x )}{x}

Simplify

e^{l n (7 x) l n (7 x)} \frac{2 ln ( 7 x )}{x} : \frac{2 e ^{l n^{2} (7 x)} ln ( 7 x )}{x}

= \frac{2 e ^{l n^{2} (7 x)} ln ( 7 x )}{x}

\int_{0}^{2 π} sin (t) d t

\frac{d}{d x} (9 lo g_{2} (x))

n \to \infty lim (e^{- n})

\frac{\partial}{\partial y} (2 x + 2 y)

e^{\frac{x}{( x - 4 )}}

What is the derivative of (7x^{ln(7x)}) ?
The derivative of (7x^{ln(7x)}) is (2e^{ln^2(7x)}ln(7x))/x
What is the first derivative of (7x^{ln(7x)}) ?
The first derivative of (7x^{ln(7x)}) is (2e^{ln^2(7x)}ln(7x))/x