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))

\frac{d}{d x} (lo g_{5} (x^{6} + x))

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

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

\int sec^{2} (3 x) e^{t a n (3 x)} d x

y^{^{'}} - y = x

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))