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

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

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

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

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

(cos (x) ln (x^{2} + 1) + \frac{2 x sin ( x )}{x ^{2} + 1}) (x^{2} + 1)^{s i n (x)}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

= (cos (x) ln (x^{2} + 1) + \frac{2 x sin ( x )}{x ^{2} + 1}) (x^{2} + 1)^{s i n (x)}

\int_{0}^{1} 2 (1 + x)^{5} d x

0.8 e^{x} arctan (x)

\int \frac{( x + 1 )}{x - 1} d x

\frac{d ^{3}}{d x ^{3}} (\frac{8}{x ^{2}})

\int 9 x e^{7 x} d x

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