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Popular >

derivative of sin(x*cos(y))

Solution

\frac{d}{d x} (sin (x) \cdot 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

sum from n=1 to infinity of-2/n

n = 1 \sum \infty - \frac{2}{n}

sum from n=1 to infinity of 1/n (x/5)^n

n = 1 \sum \infty \frac{1}{n} (\frac{x}{5})^{n}

(dP)/(dt)=0.1P-0.00013333P^2

\frac{d P}{d t} = 0.1 P - 0.00013333 P^{2}

2(ln(y))y^'-x^9y=0

2 (ln (y)) y^{^{'}} - x^{9} y = 0

derivative of f(x)=x^2-8x+16 derivative of

f (x) = x^{2} - 8 x + 16

Frequently Asked Questions (FAQ)

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