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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

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

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

\frac{1}{2 x + 1}, at a = 3

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

\frac{x ^{2} - 3 x + 2}{2 x + 1}

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