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Popular >

derivative of-sin(xy)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = sin (x), g = y

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

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

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

Simplify

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

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

Popular Examples

(\partial)/(\partial x)(-5ycos(-9x))

\frac{\partial}{\partial x} (- 5 y cos (- 9 x))

limit as x approaches infinity of 7-e^x

x \to \infty lim (7 - e^{x})

integral from 0 to 1 of (16x)/(8x^2+2)

\int_{0}^{1} \frac{16 x}{8 x ^{2} + 2} d x

integral of tan^3(x)sec^{-1/2}(x)

\int tan^{3} (x) sec^{- \frac{1}{2}} (x) d x

(\partial)/(\partial t)(sin(t))

\frac{\partial}{\partial t} (sin (t))

Frequently Asked Questions (FAQ)

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