What is the derivative of x^{x^2+1} ?

The derivative of x^{x^2+1} is x^{x^2+1}(2xln(x)+(x^2+1)/x)

What is the first derivative of x^{x^2+1} ?

The first derivative of x^{x^2+1} is x^{x^2+1}(2xln(x)+(x^2+1)/x)

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

k = 0 \sum \infty \frac{1}{( k ! ) ^{2}}

y^{^{'}} - \frac{y}{t} = t e^{t}

\int - \frac{e ^{x} sin ( x )}{2} d x

\int 30 - 10 x d x

\frac{d y}{d x} - y = 9 x

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