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Popular >

derivative of x^3cos(y)

Solution

\frac{d}{d x} (x^{3} cos (y))

Solution

3 x^{2} cos (y) - x^{3} sin (y) \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x^{3} cos (y))

Apply the Product Rule:

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

f = x^{3}, g = cos (y)

= \frac{d}{d x} (x^{3}) cos (y) + \frac{d}{d x} (cos (y)) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} cos (y) + (- sin (y) \frac{d y}{d x}) x^{3}

Simplify

= 3 x^{2} cos (y) - x^{3} sin (y) \frac{d y}{d x}

Popular Examples

derivative of ((x^2-1))/(2x-3)derivative of

\frac{( x ^{2} - 1 )}{2 x - 3}

(\partial)/(\partial y)(4x^3y^3+3)

\frac{\partial}{\partial y} (4 x^{3} y^{3} + 3)

derivative of sqrt(4x+5)

\frac{d}{d x} (4 x + 5)

integral of sin^3(4x)cos^{-2}(4x)

\int sin^{3} (4 x) cos^{- 2} (4 x) d x

integral of cot^7(x/2)csc^2(x/2)

\int cot^{7} (\frac{x}{2}) csc^{2} (\frac{x}{2}) d x

Frequently Asked Questions (FAQ)

What is the derivative of x^3cos(y) ?
The derivative of x^3cos(y) is 3x^2cos(y)-x^3sin(y)(dy)/(dx)
What is the first derivative of x^3cos(y) ?
The first derivative of x^3cos(y) is 3x^2cos(y)-x^3sin(y)(dy)/(dx)