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Popular >

derivative of cos^2(x^2+3)

Solution

\frac{d}{d x} (cos^{2} (x^{2} + 3))

Solution

- 4 x cos (x^{2} + 3) sin (x^{2} + 3)

Solution steps

\frac{d}{d x} (cos^{2} (x^{2} + 3))

Apply the chain rule:

2 cos (x^{2} + 3) \frac{d}{d x} (cos (x^{2} + 3))

= 2 cos (x^{2} + 3) \frac{d}{d x} (cos (x^{2} + 3))

\frac{d}{d x} (cos (x^{2} + 3)) = - sin (x^{2} + 3) \cdot 2 x

= 2 cos (x^{2} + 3) (- sin (x^{2} + 3) \cdot 2 x)

Simplify

= - 4 x cos (x^{2} + 3) sin (x^{2} + 3)

Popular Examples

(\partial)/(\partial y)(y-e^t)

\frac{\partial}{\partial y} (y - e^{t})

derivative of (xy+2y-x-2/(xy-3y+x-3))

\frac{d}{d x} (\frac{x y + 2 y - x - 2}{x y - 3 y + x - 3})

csc(y)dx+sec(2x)dy=0

csc (y) d x + sec (2 x) d y = 0

(\partial)/(\partial x)(cos(pi)x)

\frac{\partial}{\partial x} (cos (π) x)

(d^2)/(dx^2)((x^2)/(1+2x))

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

Frequently Asked Questions (FAQ)

What is the derivative of cos^2(x^2+3) ?
The derivative of cos^2(x^2+3) is -4xcos(x^2+3)sin(x^2+3)
What is the first derivative of cos^2(x^2+3) ?
The first derivative of cos^2(x^2+3) is -4xcos(x^2+3)sin(x^2+3)