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Popular >

derivative of sin(xsin(y))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Popular Examples

3((dy)/(dx))+12y=4

3 (\frac{d y}{d x}) + 12 y = 4

integral of (sin^3(sqrt(x)))/(sqrt(x))

\int \frac{sin ^{3} ( x )}{x} d x

(\partial)/(\partial x)(xln(z^4+x^6))

\frac{\partial}{\partial x} (x ln (z^{4} + x^{6}))

derivative of f(x)=3sqrt(x-1)derivative of

f (x) = 3 x - 1

(d^4)/(dx^4)(19e^{x^2})

\frac{d ^{4}}{d x ^{4}} (19 e^{x^{2}})

Frequently Asked Questions (FAQ)

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