en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of x^2cos(xy)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

(\frac{4}{x ^{2}})^{^{'}}

derivative of (3x^4-x^3(x^2+x^3))

\frac{d}{d x} ((3 x^{4} - x^{3}) (x^{2} + x^{3}))

(\partial)/(\partial x)(xy^3+6)

\frac{\partial}{\partial x} (x y^{3} + 6)

x^2y^'+y=0,y(8)=5

x^{2} y^{^{'}} + y = 0, y (8) = 5

integral from 0 to 3 of 1/((x+2)(x+4))

\int_{0}^{3} \frac{1}{( x + 2 ) ( x + 4 )} d x

Frequently Asked Questions (FAQ)

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