What is (\partial)/(\partial x)(4sin(x^3y^2)) ?

The answer to (\partial)/(\partial x)(4sin(x^3y^2)) is 12x^2y^2cos(x^3y^2)

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(\partial)/(\partial x)(4sin(x^3y^2))

\frac{\partial}{\partial x} (4 sin (x^{3} y^{2}))

12 x^{2} y^{2} cos (x^{3} y^{2})

Solution steps

\frac{\partial}{\partial x} (4 sin (x^{3} y^{2}))

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 4 \frac{\partial}{\partial x} (sin (x^{3} y^{2}))

Apply the chain rule:

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

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

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

= 4 cos (x^{3} y^{2}) \cdot 3 y^{2} x^{2}

Simplify

= 12 x^{2} y^{2} cos (x^{3} y^{2})

\frac{( 3 u ^{2} )}{( u ^{2} + u ) ^{3}}

\int_{1}^{2} \frac{3}{x ^{2}} - 1 d x

x \to 0 lim (\frac{x}{x})

(3, 1), (5, - 4)

\int \frac{1}{9 x ^{2} - 36 x + 37} d x

What is (\partial)/(\partial x)(4sin(x^3y^2)) ?
The answer to (\partial)/(\partial x)(4sin(x^3y^2)) is 12x^2y^2cos(x^3y^2)