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

The derivative of x^{-3}y^{-4} is -3/(x^4y^4)-(4\frac{dy)/(dx)}{x^3y^5}

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

The first derivative of x^{-3}y^{-4} is -3/(x^4y^4)-(4\frac{dy)/(dx)}{x^3y^5}

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

- \frac{3}{x ^{4} y ^{4}} - \frac{4 \frac{d y}{d x}}{x ^{3} y ^{5}}

Solution steps

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

Apply the Product Rule:

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

f = x^{- 3}, g = y^{- 4}

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

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

\frac{d}{d x} (y^{- 4}) = - \frac{4 \frac{d y}{d x}}{y ^{5}}

= (- \frac{3}{x ^{4}}) y^{- 4} + (- \frac{4 \frac{d y}{d x}}{y ^{5}}) x^{- 3}

Simplify

(- \frac{3}{x ^{4}}) y^{- 4} + (- \frac{4 \frac{d y}{d x}}{y ^{5}}) x^{- 3} : - \frac{3}{x ^{4} y ^{4}} - \frac{4 \frac{d y}{d x}}{x ^{3} y ^{5}}

= - \frac{3}{x ^{4} y ^{4}} - \frac{4 \frac{d y}{d x}}{x ^{3} y ^{5}}

n \to \infty lim (n^{0})

f (x) = 3^{(x^{5})}

y^{^{'}} + b y = 0

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

\int sinh (10 x) d x

What is the derivative of x^{-3}y^{-4} ?
The derivative of x^{-3}y^{-4} is -3/(x^4y^4)-(4\frac{dy)/(dx)}{x^3y^5}
What is the first derivative of x^{-3}y^{-4} ?
The first derivative of x^{-3}y^{-4} is -3/(x^4y^4)-(4\frac{dy)/(dx)}{x^3y^5}