What is the d/(dθ)((1+2sin(θ))sin(θ)) ?

The d/(dθ)((1+2sin(θ))sin(θ)) is cos(θ)(1+2sin(θ))+sin(2θ)

What is the first d/(dθ)((1+2sin(θ))sin(θ)) ?

The first d/(dθ)((1+2sin(θ))sin(θ)) is cos(θ)(1+2sin(θ))+sin(2θ)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d θ} ((1 + 2 sin (θ)) sin (θ))

cos (θ) (1 + 2 sin (θ)) + sin (2 θ)

Solution steps

\frac{d}{d θ} ((1 + 2 sin (θ)) sin (θ))

Apply the Product Rule:

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

f = 1 + 2 sin (θ), g = sin (θ)

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

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

\frac{d}{d θ} (sin (θ)) = cos (θ)

= 2 cos (θ) sin (θ) + cos (θ) (1 + 2 sin (θ))

Use the Double Angle identity:

2 sin (x) cos (x) = sin (2 x)

= cos (θ) (1 + 2 sin (θ)) + sin (2 θ)

\int t^{2} 1 + t^{3} d t

\int \frac{1}{sec ( y )} d y

\int \frac{( x ^{2} + 4 )}{x + 2} d x

\int \frac{1}{sin ( x ) + 3 cos ( x ) + 1} d x

\frac{d}{d x} (sin (e^{x^{3} s i n (x)}))

What is the d/(dθ)((1+2sin(θ))sin(θ)) ?
The d/(dθ)((1+2sin(θ))sin(θ)) is cos(θ)(1+2sin(θ))+sin(2θ)
What is the first d/(dθ)((1+2sin(θ))sin(θ)) ?
The first d/(dθ)((1+2sin(θ))sin(θ)) is cos(θ)(1+2sin(θ))+sin(2θ)