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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (lo g_{3} (x + 2))

y^{^{'}} = \frac{1}{e ^{- y} - x}

\int \frac{1}{( x - 2 ) ( x - 1 )} d x

\frac{7}{1 - t}

\frac{\partial}{\partial x} (t e^{- t})

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