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Popular >

derivative of 3^{x^2}

Solution

derivative of

3^{x^{2}}

Solution

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

Solution steps

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

Apply exponent rule:

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

3^{x^{2}} = e^{x^{2} l n (3)}

= \frac{d}{d x} (e^{x^{2} l n (3)})

Apply the chain rule:

e^{x^{2} l n (3)} \frac{d}{d x} (x^{2} ln (3))

= e^{x^{2} l n (3)} \frac{d}{d x} (x^{2} ln (3))

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

= e^{x^{2} l n (3)} \cdot 2 ln (3) x

e^{x^{2} l n (3)} = 3^{x^{2}}

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

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Frequently Asked Questions (FAQ)

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