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Popular >

derivative of |cos(x|)

Solution

\frac{d}{d x} (∣ cos (x) ∣)

Solution

- \frac{cos ( x ) sin ( x )}{∣ cos ( x ) ∣}

Solution steps

\frac{d}{d x} (∣ cos (x) ∣)

Apply the chain rule:

\frac{cos ( x )}{∣ cos ( x ) ∣} \frac{d}{d x} (cos (x))

= \frac{cos ( x )}{∣ cos ( x ) ∣} \frac{d}{d x} (cos (x))

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

= \frac{cos ( x )}{∣ cos ( x ) ∣} (- sin (x))

Simplify

\frac{cos ( x )}{∣ cos ( x ) ∣} (- sin (x)) : - \frac{cos ( x ) sin ( x )}{∣ cos ( x ) ∣}

= - \frac{cos ( x ) sin ( x )}{∣ cos ( x ) ∣}

Graph

Popular Examples

(y^3-1)e^xdx+3y^2(e^x+1)dy=0,y(0)=-2

(y^{3} - 1) e^{x} d x + 3 y^{2} (e^{x} + 1) d y = 0, y (0) = - 2

integral of sqrt(3x^2+5)

\int 3 x^{2} + 5 d x

(\partial)/(\partial x)(sqrt(9-x^3-y^5))

\frac{\partial}{\partial x} (9 - x^{3} - y^{5})

derivative of 6^{4-3x}

\frac{d}{d x} (6^{4 - 3 x})

derivative of x/(sqrt(x^2+49))

\frac{d}{d x} (\frac{x}{x ^{2} + 49})

Frequently Asked Questions (FAQ)

What is the derivative of |cos(x|) ?
The derivative of |cos(x|) is -(cos(x)sin(x))/(|cos(x)|)
What is the first derivative of |cos(x|) ?
The first derivative of |cos(x|) is -(cos(x)sin(x))/(|cos(x)|)