What is the derivative of (a(e^{ax^6})) ?

The derivative of (a(e^{ax^6})) is 6a^2e^{ax^6}x^5

What is the first derivative of (a(e^{ax^6})) ?

The first derivative of (a(e^{ax^6})) is 6a^2e^{ax^6}x^5

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\frac{d}{d x} ((a) (e^{a x^{6}}))

6 a^{2} e^{a x^{6}} x^{5}

Solution steps

\frac{d}{d x} ((a) (e^{a x^{6}}))

Take the constant out:

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

= a \frac{d}{d x} (e^{a x^{6}})

Apply the chain rule:

e^{a x^{6}} \frac{d}{d x} (a x^{6})

= e^{a x^{6}} \frac{d}{d x} (a x^{6})

\frac{d}{d x} (a x^{6}) = 6 a x^{5}

= a e^{a x^{6}} \cdot 6 a x^{5}

Simplify

a e^{a x^{6}} \cdot 6 a x^{5} : 6 a^{2} e^{a x^{6}} x^{5}

= 6 a^{2} e^{a x^{6}} x^{5}

3 a x + b x + 3 a y + b y

a r - 2 b r - 2 a y + 4 b y

36 x^{2} - 4 π x^{2}

[(A r - s) + 2] [(A r - s) - 2]

6 e - 8

What is the derivative of (a(e^{ax^6})) ?
The derivative of (a(e^{ax^6})) is 6a^2e^{ax^6}x^5
What is the first derivative of (a(e^{ax^6})) ?
The first derivative of (a(e^{ax^6})) is 6a^2e^{ax^6}x^5