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))

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

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))

n = 0 \sum \infty \frac{5 n}{2 n - 1}

y^{^{'}} + 3 y = e^{- 3 x}

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

\frac{\partial}{\partial x} (x^{9} y z^{2} + 9 yz)

\frac{\partial}{\partial y} (y^{2} x)

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))