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

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

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

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

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

f (x) = x^{2} + a x + 2, at x = 1

\int - 6 ln (x^{2} - 1) d x

\int (x cos (4 x)) d x

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

\int \frac{1 + y ^{2}}{1 + x ^{2}} d x

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