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

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derivative of

(x^{2} + x)^{x}

(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}

\frac{d}{d x} (ln (x^{2} + y^{2}) f (x, y))

cot (2 x + 1)

\frac{( x ^{5} )}{5} - \frac{( 16 x ^{3} )}{3} + 7

\frac{d}{d t} (4 + 3 t + 2 t^{2})

p + 1

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