What is the derivative of-3e^{x^5} ?

The derivative of-3e^{x^5} is -15e^{x^5}x^4

What is the first derivative of-3e^{x^5} ?

The first derivative of-3e^{x^5} is -15e^{x^5}x^4

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derivative of

- 3 e^{x^{5}}

- 15 e^{x^{5}} x^{4}

Solution steps

\frac{d}{d x} (- 3 e^{x^{5}})

Take the constant out:

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

= - 3 \frac{d}{d x} (e^{x^{5}})

Apply the chain rule:

e^{x^{5}} \frac{d}{d x} (x^{5})

= e^{x^{5}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= - 3 e^{x^{5}} \cdot 5 x^{4}

Simplify

= - 15 e^{x^{5}} x^{4}

What is the derivative of-3e^{x^5} ?
The derivative of-3e^{x^5} is -15e^{x^5}x^4
What is the first derivative of-3e^{x^5} ?
The first derivative of-3e^{x^5} is -15e^{x^5}x^4