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Popular >

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

Solution

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

Solution

- sin (x) + cos (2 x) \cdot 2

Solution steps

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

Simplify

cos (x) + 2 sin (x) cos (x) : cos (x) + sin (2 x)

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

Apply the Sum/Difference Rule:

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

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

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

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

= - sin (x) + cos (2 x) \cdot 2

Popular Examples

integral of w/(1+w^2)

\int \frac{w}{1 + w ^{2}} d w

derivative of x/(x^2+14x+45)derivative of

\frac{x}{x ^{2} + 14 x + 45}

derivative of e^{(-5x^3-2x^2})

\frac{d}{d x} (e^{(- 5 x^{3} - 2 x^{2})})

(dy)/(dx)=3x^2(1+y^2)^{3/2}

\frac{d y}{d x} = 3 x^{2} (1 + y^{2})^{\frac{3}{2}}

derivative of f(x)=5x^2-x^{1/3}derivative of

f (x) = 5 x^{2} - x^{\frac{1}{3}}

Frequently Asked Questions (FAQ)

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