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Popular >

derivative of 3^{2x^2}

Solution

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

Solution

4 ln (3) \cdot 9^{x^{2}} x

Solution steps

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

Simplify

3^{2 x^{2}} : 9^{x^{2}}

= \frac{d}{d x} (9^{x^{2}})

Apply exponent rule:

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

9^{x^{2}} = e^{x^{2} l n (9)}

= \frac{d}{d x} (e^{x^{2} l n (9)})

Apply the chain rule:

e^{x^{2} l n (9)} \frac{d}{d x} (x^{2} ln (9))

= e^{x^{2} l n (9)} \frac{d}{d x} (x^{2} ln (9))

\frac{d}{d x} (x^{2} ln (9)) = 4 ln (3) x

= e^{x^{2} l n (9)} \cdot 4 ln (3) x

e^{x^{2} l n (9)} = 9^{x^{2}}

= 4 ln (3) \cdot 9^{x^{2}} x

Popular Examples

(\partial)/(\partial x)(e^{7x^2+5y^2})

\frac{\partial}{\partial x} (e^{7 x^{2} + 5 y^{2}})

integral of 4csc^2(x)

\int 4 csc^{2} (x) d x

tangent of f(x)=4x^2-2x+1 tangent of

f (x) = 4 x^{2} - 2 x + 1

integral of (5x^4)/(1+x^5)

\int \frac{5 x ^{4}}{1 + x ^{5}} d x

tangent of f(x)=sqrt(2x+1),\at x=3 tangent of

f (x) = 2 x + 1, at x = 3

Frequently Asked Questions (FAQ)

What is the derivative of 3^{2x^2} ?
The derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x
What is the first derivative of 3^{2x^2} ?
The first derivative of 3^{2x^2} is 4ln(3)*9^{x^2}x