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

The derivative of sin^2(x^2+1) is 4xsin(x^2+1)cos(x^2+1)

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

The first derivative of sin^2(x^2+1) is 4xsin(x^2+1)cos(x^2+1)

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derivative of

sin^{2} (x^{2} + 1)

4 x sin (x^{2} + 1) cos (x^{2} + 1)

Solution steps

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

Apply the chain rule:

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

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

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

= 2 sin (x^{2} + 1) cos (x^{2} + 1) \cdot 2 x

Simplify

= 4 x sin (x^{2} + 1) cos (x^{2} + 1)

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

\frac{x ^{5}}{2}

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

\frac{4 ln ( x + 2 )}{x ^{2}}

f (x) = 2 x^{3} - 5 x^{2} + 10 x + 2

What is the derivative of sin^2(x^2+1) ?
The derivative of sin^2(x^2+1) is 4xsin(x^2+1)cos(x^2+1)
What is the first derivative of sin^2(x^2+1) ?
The first derivative of sin^2(x^2+1) is 4xsin(x^2+1)cos(x^2+1)