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Popular >

derivative of 3^{(x^5})

Solution

\frac{d}{d x} (3^{(x^{5})})

Solution

5 ln (3) \cdot 3^{x^{5}} x^{4}

Solution steps

\frac{d}{d x} (3^{(x^{5})})

Apply exponent rule:

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

3^{x^{5}} = e^{x^{5} l n (3)}

= \frac{d}{d x} (e^{x^{5} l n (3)})

Apply the chain rule:

e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

= e^{x^{5} l n (3)} \frac{d}{d x} (x^{5} ln (3))

\frac{d}{d x} (x^{5} ln (3)) = 5 ln (3) x^{4}

= e^{x^{5} l n (3)} \cdot 5 ln (3) x^{4}

e^{x^{5} l n (3)} = 3^{x^{5}}

= 5 ln (3) \cdot 3^{x^{5}} x^{4}

Popular Examples

integral from 0 to 1 of 1/(sqrt(9-x^2))

\int_{0}^{1} \frac{1}{9 - x ^{2}} d x

(\partial)/(\partial x)(tan(x)arcsin(x))

\frac{\partial}{\partial x} (tan (x) arcsin (x))

integral of sqrt(x^2+x^4)

\int x^{2} + x^{4} d x

integral from 0 to 3 of 2x-x^2

\int_{0}^{3} 2 x - x^{2} d x

limit as x approaches 5 of (x+3)/(x-3)

x \to 5 lim (\frac{x + 3}{x - 3})

Frequently Asked Questions (FAQ)

What is the derivative of 3^{(x^5}) ?
The derivative of 3^{(x^5}) is 5ln(3)*3^{x^5}x^4
What is the first derivative of 3^{(x^5}) ?
The first derivative of 3^{(x^5}) is 5ln(3)*3^{x^5}x^4