What is the derivative of y=(sin(x+y))^2 ?

The derivative of y=(sin(x+y))^2 is sin(2x+2y)

What is the first derivative of y=(sin(x+y))^2 ?

The first derivative of y=(sin(x+y))^2 is sin(2x+2y)

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derivative of

y = (sin (x + y))^{2}

sin (2 x + 2 y)

Solution steps

\frac{d}{d x} ((sin (x + y))^{2})

Treat

y

as a constant

Apply the chain rule:

2 sin (x + y) \frac{d}{d x} (sin (x + y))

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

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

= 2 sin (x + y) cos (x + y)

Simplify

2 sin (x + y) cos (x + y) : sin (2 x + 2 y)

= sin (2 x + 2 y)

\frac{- x}{2}

2 - cos^{3} (x)

60 q - 2 q^{2}

\frac{- 1}{y}

\frac{d}{d t} (3.5 t^{2} + 41 t + 9)

What is the derivative of y=(sin(x+y))^2 ?
The derivative of y=(sin(x+y))^2 is sin(2x+2y)
What is the first derivative of y=(sin(x+y))^2 ?
The first derivative of y=(sin(x+y))^2 is sin(2x+2y)