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Popular >

derivative of sin(xcos(y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = cos (y)

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

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

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

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

Simplify

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

Popular Examples

integral of (x^2+x+x^{-3})

\int (x^{2} + x + x^{- 3}) d x

derivative of x/(sqrt(x^2-9))

\frac{d}{d x} (\frac{x}{x ^{2} - 9})

integral of 1/(64e^{-7x)+e^{7x}}

\int \frac{1}{64 e ^{- 7 x} + e ^{7 x}} d x

limit as x approaches 0 of 5/(x+x^2)

x \to 0 lim (\frac{5}{x + x ^{2}})

derivative of f(x)=10x+6 derivative of

f (x) = 10 x + 6

Frequently Asked Questions (FAQ)

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