What is the derivative of (1+2sin(x)cos(x)) ?

The derivative of (1+2sin(x)cos(x)) is 2cos^2(x)-sin(x)(1+2sin(x))

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

The first derivative of (1+2sin(x)cos(x)) is 2cos^2(x)-sin(x)(1+2sin(x))

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

2 cos^{2} (x) - sin (x) (1 + 2 sin (x))

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

2 cos (x) cos (x) + (- sin (x)) (1 + 2 sin (x)) : 2 cos^{2} (x) - sin (x) (1 + 2 sin (x))

= 2 cos^{2} (x) - sin (x) (1 + 2 sin (x))

n = 1 \sum \infty \frac{n}{( n + 1 ) 3 ^{n}}

\int cos^{2} (x) \cdot sin (2 x) d x

\int \frac{- x - 1}{2 ( x ^{2} + 1 )} d x

\int 20 cot^{4} (x) d x

\frac{\partial}{\partial x} (10 x^{3} + 3 x^{2} y - 3 y^{5})

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