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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

\frac{1}{s ( s + 4 ) ( s + 2 )}

\int \frac{ln ( 3 x + 1 )}{12 x + 4} d x

\frac{d ^{2}}{d x ^{2}} (x (x - 4)^{3})

e^{a x}

\int 5 x^{5} - x d x

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