What is the derivative of-10ln(xe^{x^8}) ?

The derivative of-10ln(xe^{x^8}) is -10(1/x+8x^7)

What is the first derivative of-10ln(xe^{x^8}) ?

The first derivative of-10ln(xe^{x^8}) is -10(1/x+8x^7)

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derivative of

- 10 ln (x e^{x^{8}})

- 10 (\frac{1}{x} + 8 x^{7})

Solution steps

\frac{d}{d x} (- 10 ln (x e^{x^{8}}))

Simplify

- 10 ln (x e^{x^{8}}) : - 10 (ln (x) + x^{8})

= \frac{d}{d x} (- 10 (ln (x) + x^{8}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 10 \frac{d}{d x} (ln (x) + x^{8})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - 10 (\frac{d}{d x} (ln (x)) + \frac{d}{d x} (x^{8}))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (x^{8}) = 8 x^{7}

= - 10 (\frac{1}{x} + 8 x^{7})

What is the derivative of-10ln(xe^{x^8}) ?
The derivative of-10ln(xe^{x^8}) is -10(1/x+8x^7)
What is the first derivative of-10ln(xe^{x^8}) ?
The first derivative of-10ln(xe^{x^8}) is -10(1/x+8x^7)