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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Popular Examples

(\partial)/(\partial x)(2/(2x-y))

\frac{\partial}{\partial x} (\frac{2}{2 x - y})

integral from 1 to infinity of 1/(x^2+5)

\int_{1}^{\infty} \frac{1}{x ^{2} + 5} d x

laplacetransform 5^t laplace transform

5^{t}

tangent of f(x)=sqrt(x+3),\at x=1 tangent of

f (x) = x + 3, at x = 1

derivative of (ln(x^5)/(ln(x^4)))

\frac{d}{d x} (\frac{ln ( x ^{5} )}{ln ( x ^{4} )})

Frequently Asked Questions (FAQ)

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