What is the derivative of 4x^3y^{-2} ?

The derivative of 4x^3y^{-2} is 4((3x^2)/(y^2)-(2x^3\frac{dy)/(dx)}{y^3})

What is the first derivative of 4x^3y^{-2} ?

The first derivative of 4x^3y^{-2} is 4((3x^2)/(y^2)-(2x^3\frac{dy)/(dx)}{y^3})

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Popular >

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{3}, g = y^{- 2}

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

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

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

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

Simplify

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

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

\frac{d}{d x} (cos^{n} (x))

\frac{\partial}{\partial x} (- x)

\frac{d}{d x} (\frac{x}{e ^{x} - 100 x})

r

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

What is the derivative of 4x^3y^{-2} ?
The derivative of 4x^3y^{-2} is 4((3x^2)/(y^2)-(2x^3\frac{dy)/(dx)}{y^3})
What is the first derivative of 4x^3y^{-2} ?
The first derivative of 4x^3y^{-2} is 4((3x^2)/(y^2)-(2x^3\frac{dy)/(dx)}{y^3})