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Popular >

d/(dy)(-x^2y^2sin(x)+2xy^2cos(x))

Solution

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

Solution

- 2 x^{2} y sin (x) + 4 x y cos (x)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d y} (2 x y^{2} cos (x)) = 4 x y cos (x)

= - 2 x^{2} y sin (x) + 4 x y cos (x)

Popular Examples

integral of sqrt(x/(1-x))

\int \frac{x}{1 - x} d x

y^{^{'}} = 3 - y

integral of (7x^3-3x^2+21x+6)/(x^3+3x)

\int \frac{7 x ^{3} - 3 x ^{2} + 21 x + 6}{x ^{3} + 3 x} d x

(dy)/(dx)+3x^2y=sin(x)e^{-x^3}

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

derivative of cos(sqrt(sin(tan(2pix))))

\frac{d}{d x} (cos (sin (tan (2 π x))))

Frequently Asked Questions (FAQ)

What is the d/(dy)(-x^2y^2sin(x)+2xy^2cos(x)) ?
The d/(dy)(-x^2y^2sin(x)+2xy^2cos(x)) is -2x^2ysin(x)+4xycos(x)
What is the first d/(dy)(-x^2y^2sin(x)+2xy^2cos(x)) ?
The first d/(dy)(-x^2y^2sin(x)+2xy^2cos(x)) is -2x^2ysin(x)+4xycos(x)