What is the derivative of y=(e^{4x^{2+1}})/8 ?

The derivative of y=(e^{4x^{2+1}})/8 is (3e^{4x^3}x^2)/2

What is the first derivative of y=(e^{4x^{2+1}})/8 ?

The first derivative of y=(e^{4x^{2+1}})/8 is (3e^{4x^3}x^2)/2

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derivative of

y = \frac{e ^{4 x^{2 + 1}}}{8}

\frac{3 e ^{4 x^{3}} x ^{2}}{2}

Solution steps

\frac{d}{d x} (\frac{e ^{4 x^{2 + 1}}}{8})

Take the constant out:

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

= \frac{1}{8} \frac{d}{d x} (e^{4 x^{2 + 1}})

Apply the chain rule:

e^{4 x^{2 + 1}} \frac{d}{d x} (4 x^{2 + 1})

= e^{4 x^{2 + 1}} \frac{d}{d x} (4 x^{2 + 1})

\frac{d}{d x} (4 x^{2 + 1}) = 12 x^{2}

= \frac{1}{8} e^{4 x^{2 + 1}} \cdot 12 x^{2}

Simplify

\frac{1}{8} e^{4 x^{2 + 1}} \cdot 12 x^{2} : \frac{3 e ^{4 x^{3}} x ^{2}}{2}

= \frac{3 e ^{4 x^{3}} x ^{2}}{2}

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What is the derivative of y=(e^{4x^{2+1}})/8 ?
The derivative of y=(e^{4x^{2+1}})/8 is (3e^{4x^3}x^2)/2
What is the first derivative of y=(e^{4x^{2+1}})/8 ?
The first derivative of y=(e^{4x^{2+1}})/8 is (3e^{4x^3}x^2)/2