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Popular >

derivative of x^{9x}

Solution

derivative of

x^{9 x}

Solution

9 x^{9 x} (ln (x) + 1)

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (9 x ln (x)) = 9 (ln (x) + 1)

= e^{9 x l n (x)} \cdot 9 (ln (x) + 1)

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

= 9 x^{9 x} (ln (x) + 1)

Popular Examples

y^'+8(tan(8x))*y=-9cos(8x)

y^{^{'}} + 8 (tan (8 x)) \cdot y = - 9 cos (8 x)

slope ofintercept (0.5)(7.9)slope intercept

(0.5) (7.9)

integral of 9e^{5x+e^{5x}}

\int 9 e^{5 x + e^{5 x}} d x

integral of x(4x-1)^4

\int x (4 x - 1)^{4} d x

integral of 1/(sqrt(4+(u+3)))

\int \frac{1}{4 + ( u + 3 )} d u

Frequently Asked Questions (FAQ)

What is the derivative of x^{9x} ?
The derivative of x^{9x} is 9x^{9x}(ln(x)+1)
What is the first derivative of x^{9x} ?
The first derivative of x^{9x} is 9x^{9x}(ln(x)+1)