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Popular >

derivative of x^2cos(y)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = cos (y)

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

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

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

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

Simplify

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

Popular Examples

derivative of (x^2+18(2x+15))

\frac{d}{d x} ((x^{2} + 18) (2 x + 15))

derivative of y=x^3(9-x^2)derivative of

y = x^{3} (9 - x^{2})

derivative of 2x^7+3x+11 derivative of

2 x^{7} + 3 x + 11

(\partial)/(\partial x)(x/(2*sqrt(2)))

\frac{\partial}{\partial x} (\frac{x}{2 \cdot 2})

1+y^2+2(t+1)y(dy)/(dt)=0,y(0)=1

1 + y^{2} + 2 (t + 1) y \frac{d y}{d t} = 0, y (0) = 1

Frequently Asked Questions (FAQ)

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