What is the d/(dy)(3x(5+y)^{-1}) ?

The d/(dy)(3x(5+y)^{-1}) is -(3x)/((5+y)^2)

What is the first d/(dy)(3x(5+y)^{-1}) ?

The first d/(dy)(3x(5+y)^{-1}) is -(3x)/((5+y)^2)

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\frac{d}{d y} (3 x (5 + y)^{- 1})

- \frac{3 x}{( 5 + y ) ^{2}}

Solution steps

\frac{d}{d y} (3 x (5 + y)^{- 1})

Treat

x

as a constant

Take the constant out:

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

= 3 x \frac{d}{d y} ((5 + y)^{- 1})

Apply the chain rule:

- \frac{1}{( 5 + y ) ^{2}} \frac{d}{d y} (5 + y)

= - \frac{1}{( 5 + y ) ^{2}} \frac{d}{d y} (5 + y)

\frac{d}{d y} (5 + y) = 1

= 3 x (- \frac{1}{( 5 + y ) ^{2}} \cdot 1)

Simplify

3 x (- \frac{1}{( 5 + y ) ^{2}} \cdot 1) : - \frac{3 x}{( 5 + y ) ^{2}}

= - \frac{3 x}{( 5 + y ) ^{2}}

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

\int \frac{1}{4 x ^{2} - 16 x + 52} d x

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

y^{^{'}} = 10 y

\frac{d}{d x} (x - \frac{1}{7} x)

What is the d/(dy)(3x(5+y)^{-1}) ?
The d/(dy)(3x(5+y)^{-1}) is -(3x)/((5+y)^2)
What is the first d/(dy)(3x(5+y)^{-1}) ?
The first d/(dy)(3x(5+y)^{-1}) is -(3x)/((5+y)^2)