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Popular >

derivative of sin(x^2+sin^2(x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

(\partial ^2)/(\partial z^2)(x^2y^4e^z+3y^3e^{xz}+2e^{xyz}+3y)

\frac{\partial ^{2}}{\partial z ^{2}} (x^{2} y^{4} e^{z} + 3 y^{3} e^{x z} + 2 e^{x yz} + 3 y)

y^'=((y^4+3))/(4xy^3)

y^{^{'}} = \frac{( y ^{4} + 3 )}{4 x y ^{3}}

(dy)/(dx)=x^2*y^2

\frac{d y}{d x} = x^{2} \cdot y^{2}

integral of 1/(v^2-4)

\int \frac{1}{v ^{2} - 4} d v

integral of (2x+5)

\int (2 x + 5) d x

Frequently Asked Questions (FAQ)

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