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Popular >

derivative of (x^2+x^x)

Solution

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

Solution

(ln (x^{2} + x) + \frac{2 x + 1}{x + 1}) (x^{2} + x)^{x}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x ln (x^{2} + x)) = ln (x^{2} + x) + \frac{2 x + 1}{x + 1}

= e^{x l n (x^{2} + x)} (ln (x^{2} + x) + \frac{2 x + 1}{x + 1})

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

= (ln (x^{2} + x) + \frac{2 x + 1}{x + 1}) (x^{2} + x)^{x}

Graph

Popular Examples

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x \to \infty lim (e^{p x} (a cos (q (x) x) + b sin (q (x) x)))

(dy)/(dx)=4+e^{y-4x+5}

\frac{d y}{d x} = 4 + e^{y - 4 x + 5}

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\int x^{2} \cdot e^{3 x} d x

derivative of \sqrt[4]{3x^2-5x+2}

\frac{d}{d x} (4 3 x^{2} - 5 x + 2)

y^{''}+2y^'+y=4e^{-t},y(0)=2,y^'(0)=-1

y^{^{''}} + 2 y^{^{'}} + y = 4 e^{- t}, y (0) = 2, y^{^{'}} (0) = - 1

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+x^x) ?
The derivative of (x^2+x^x) is (ln(x^2+x)+(2x+1)/(x+1))(x^2+x)^x
What is the first derivative of (x^2+x^x) ?
The first derivative of (x^2+x^x) is (ln(x^2+x)+(2x+1)/(x+1))(x^2+x)^x