What is the derivative of 1/(yx^2) ?

The derivative of 1/(yx^2) is -(x\frac{dy)/(dx)+2y}{x^3y^2}

What is the first derivative of 1/(yx^2) ?

The first derivative of 1/(yx^2) is -(x\frac{dy)/(dx)+2y}{x^3y^2}

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\frac{d}{d x} (\frac{1}{y x ^{2}})

- \frac{x \frac{d y}{d x} + 2 y}{x ^{3} y ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{y x ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

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

= - \frac{1}{( y x ^{2} ) ^{2}} (\frac{d y}{d x} x^{2} + 2 x y)

Simplify

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

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

\int + 7 x cos (4 x) d x

\int cos (π \cdot x) d x

f (x) = x^{4} - 5 x^{2} + 4, at x = - 2

y = sin (3) x^{2}

\int (ln (x) + x) d x

What is the derivative of 1/(yx^2) ?
The derivative of 1/(yx^2) is -(x\frac{dy)/(dx)+2y}{x^3y^2}
What is the first derivative of 1/(yx^2) ?
The first derivative of 1/(yx^2) is -(x\frac{dy)/(dx)+2y}{x^3y^2}