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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

\frac{1}{( x - 2 )}

\frac{d}{d x} (\frac{cos ( x ) - 1}{sin ( x )})

(2 e^{- t}) (cos (4 t)) (1 (t))

f (x) = 2 x^{3} + 3 x^{2} + 4 x + 2, at x = - 1

y^{^{''}} + 3 y^{^{'}} = 9 x

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