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Popular >

derivative of 3^{(x^5)}

Solution

derivative of

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

sum from n=0 to infinity of sqrt(1+n)

n = 0 \sum \infty 1 + n

y^'+2y=4,y(0)=4

y^{^{'}} + 2 y = 4, y (0) = 4

derivative of 1/2 tan(x)

\frac{d}{d x} (\frac{1}{2} tan (x))

integral from 6 to 8 of (50)/((x-6)^3)

\int_{6}^{8} \frac{50}{( x - 6 ) ^{3}} d x

limit as x approaches 0 of 9/(x^2)

x \to 0 lim (\frac{9}{x ^{2}})

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