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Popular >

derivative of x^{3x}

Solution

derivative of

x^{3 x}

Solution

3 x^{3 x} (ln (x) + 1)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (3 x ln (x)) = 3 (ln (x) + 1)

= e^{3 x l n (x)} \cdot 3 (ln (x) + 1)

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

= 3 x^{3 x} (ln (x) + 1)

Popular Examples

derivative of (8x/(5-tan(x)))

\frac{d}{d x} (\frac{8 x}{5 - tan ( x )})

y^'-6/x y=x^{-4}y^5,y(1)=1

y^{^{'}} - \frac{6}{x} y = x^{- 4} y^{5}, y (1) = 1

integral from 0 to infinity of 4e^{-4x}

\int_{0}^{\infty} 4 e^{- 4 x} d x

integral of (sqrt(x))/(sqrt(x)-2)

\int \frac{x}{x - 2} d x

limit as x approaches-2 of (5x^2+6x-8)/(x+2)

x \to - 2 lim (\frac{5 x ^{2} + 6 x - 8}{x + 2})

Frequently Asked Questions (FAQ)

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