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

The derivative of sin(x+y) is cos(x+y)(1+(dy)/(dx))

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

The first derivative of sin(x+y) is cos(x+y)(1+(dy)/(dx))

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

cos (x + y) (1 + \frac{d y}{d x})

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + y) = 1 + \frac{d y}{d x}

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

What is the derivative of sin(x+y) ?
The derivative of sin(x+y) is cos(x+y)(1+(dy)/(dx))
What is the first derivative of sin(x+y) ?
The first derivative of sin(x+y) is cos(x+y)(1+(dy)/(dx))