What is the derivative of (xy^3+x^2y^3) ?

The derivative of (xy^3+x^2y^3) is 3(xy^3+x^2y)^2(y^3+3xy^2(dy)/(dx)+2xy+(dy)/(dx)x^2)

What is the first derivative of (xy^3+x^2y^3) ?

The first derivative of (xy^3+x^2y^3) is 3(xy^3+x^2y)^2(y^3+3xy^2(dy)/(dx)+2xy+(dy)/(dx)x^2)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

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

\int \frac{1}{9 x + 7} d x

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

\int (\frac{9}{x} - \frac{4}{x ^{3}}) d x

\frac{d}{d θ} (cos (θ) - sin (θ))

im pl i c i t \frac{d y}{d x}, y^{3} = x^{4}

What is the derivative of (xy^3+x^2y^3) ?
The derivative of (xy^3+x^2y^3) is 3(xy^3+x^2y)^2(y^3+3xy^2(dy)/(dx)+2xy+(dy)/(dx)x^2)
What is the first derivative of (xy^3+x^2y^3) ?
The first derivative of (xy^3+x^2y^3) is 3(xy^3+x^2y)^2(y^3+3xy^2(dy)/(dx)+2xy+(dy)/(dx)x^2)