What is the derivative of 2^{3x^2} ?

The derivative of 2^{3x^2} is 3ln(2)*2^{3x^2+1}x

What is the first derivative of 2^{3x^2} ?

The first derivative of 2^{3x^2} is 3ln(2)*2^{3x^2+1}x

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derivative of

2^{3 x^{2}}

3 ln (2) \cdot 2^{3 x^{2} + 1} x

Solution steps

\frac{d}{d x} (2^{3 x^{2}})

Simplify

2^{3 x^{2}} : 8^{x^{2}}

= \frac{d}{d x} (8^{x^{2}})

Apply exponent rule:

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

8^{x^{2}} = e^{x^{2} l n (8)}

= \frac{d}{d x} (e^{x^{2} l n (8)})

Apply the chain rule:

e^{x^{2} l n (8)} \frac{d}{d x} (x^{2} ln (8))

= e^{x^{2} l n (8)} \frac{d}{d x} (x^{2} ln (8))

\frac{d}{d x} (x^{2} ln (8)) = 6 ln (2) x

= e^{x^{2} l n (8)} \cdot 6 ln (2) x

Simplify

e^{x^{2} l n (8)} \cdot 6 ln (2) x : 3 ln (2) \cdot 2^{3 x^{2} + 1} x

= 3 ln (2) \cdot 2^{3 x^{2} + 1} x

\int \frac{cos ( 2 x )}{sin ^{2} ( 2 x )} d x

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\int_{0}^{1} \frac{3 y}{e ^{2 y}} d y

What is the derivative of 2^{3x^2} ?
The derivative of 2^{3x^2} is 3ln(2)*2^{3x^2+1}x
What is the first derivative of 2^{3x^2} ?
The first derivative of 2^{3x^2} is 3ln(2)*2^{3x^2+1}x