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Popular >

derivative of sqrt(cos(x^2))

Solution

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

Solution

- x sin (x^{2}) sec (x^{2})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 cos ( x ^{2} )} (- sin (x^{2}) \cdot 2 x) : - x sin (x^{2}) sec (x^{2})

= - x sin (x^{2}) sec (x^{2})

Popular Examples

integral from 0 to 3 of 1/(x^2-x-2)

\int_{0}^{3} \frac{1}{x ^{2} - x - 2} d x

limit as x approaches 3 of 3x^2-2x+5

x \to 3 lim (3 x^{2} - 2 x + 5)

integral of (sin(x))/(sqrt(cos(x)))

\int \frac{sin ( x )}{cos ( x )} d x

integral of 2(3x+4)^{-4}

\int 2 (3 x + 4)^{- 4} d x

tangent of f(x)= x/(x+1),(1,2)tangent of

f (x) = \frac{x}{x + 1}, (1, 2)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(cos(x^2)) ?
The derivative of sqrt(cos(x^2)) is -xsin(x^2)sqrt(sec(x^2))
What is the first derivative of sqrt(cos(x^2)) ?
The first derivative of sqrt(cos(x^2)) is -xsin(x^2)sqrt(sec(x^2))