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Popular >

derivative of (1+sin(x)*cos(2x))

Solution

\frac{d}{d x} ((1 + sin (x)) \cdot cos (2 x))

Solution

cos (x) cos (2 x) - 2 sin (2 x) (1 + sin (x))

Solution steps

\frac{d}{d x} ((1 + sin (x)) cos (2 x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + sin (x), g = cos (2 x)

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

\frac{d}{d x} (1 + sin (x)) = cos (x)

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

= cos (x) cos (2 x) + (- sin (2 x) \cdot 2) (1 + sin (x))

Simplify

= cos (x) cos (2 x) - 2 sin (2 x) (1 + sin (x))

Popular Examples

integral of (2x^2+3x+7)/(x^3+3x)

\int \frac{2 x ^{2} + 3 x + 7}{x ^{3} + 3 x} d x

(dy)/(dx)=(cos(x))e^{y+sin(x)},y(0)=0

\frac{d y}{d x} = (cos (x)) e^{y + s i n (x)}, y (0) = 0

y^{''}-3y^'+2y=0,y(0)=-1/5 ,y^'(0)=-8/5

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = - \frac{1}{5}, y^{^{'}} (0) = - \frac{8}{5}

laplacetransform 3e^{2t}sin(4t)laplace transform

3 e^{2 t} sin (4 t)

(\partial)/(\partial β)(sin(α)cos(β))

\frac{\partial}{\partial β} (sin (α) cos (β))

Frequently Asked Questions (FAQ)

What is the derivative of (1+sin(x)*cos(2x)) ?
The derivative of (1+sin(x)*cos(2x)) is cos(x)cos(2x)-2sin(2x)(1+sin(x))
What is the first derivative of (1+sin(x)*cos(2x)) ?
The first derivative of (1+sin(x)*cos(2x)) is cos(x)cos(2x)-2sin(2x)(1+sin(x))