What is the derivative of ((2y+3/(4x+5))^2) ?

The derivative of ((2y+3/(4x+5))^2) is (2(2y+3)(2\frac{dy)/(dx)(4x+5)-4(2y+3))}{(4x+5)^3}

What is the first derivative of ((2y+3/(4x+5))^2) ?

The first derivative of ((2y+3/(4x+5))^2) is (2(2y+3)(2\frac{dy)/(dx)(4x+5)-4(2y+3))}{(4x+5)^3}

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\frac{d}{d x} ((\frac{2 y + 3}{4 x + 5})^{2})

\frac{2 ( 2 y + 3 ) ( 2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 ) )}{( 4 x + 5 ) ^{3}}

Solution steps

\frac{d}{d x} ((\frac{2 y + 3}{4 x + 5})^{2})

Apply the chain rule:

2 \cdot \frac{2 y + 3}{4 x + 5} \frac{d}{d x} (\frac{2 y + 3}{4 x + 5})

= 2 \cdot \frac{2 y + 3}{4 x + 5} \frac{d}{d x} (\frac{2 y + 3}{4 x + 5})

\frac{d}{d x} (\frac{2 y + 3}{4 x + 5}) = \frac{2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 )}{( 4 x + 5 ) ^{2}}

= 2 \cdot \frac{2 y + 3}{4 x + 5} \cdot \frac{2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 )}{( 4 x + 5 ) ^{2}}

Simplify

2 \cdot \frac{2 y + 3}{4 x + 5} \cdot \frac{2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 )}{( 4 x + 5 ) ^{2}} : \frac{2 ( 2 y + 3 ) ( 2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 ) )}{( 4 x + 5 ) ^{3}}

= \frac{2 ( 2 y + 3 ) ( 2 \frac{d y}{d x} ( 4 x + 5 ) - 4 ( 2 y + 3 ) )}{( 4 x + 5 ) ^{3}}

f (x) = \frac{4 x}{x - 5}, (7, 14)

\frac{d u}{d x}

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

n = 0 \sum \infty n^{2} + n

x \to 0 lim (\frac{x}{e ^{x} - 1})

What is the derivative of ((2y+3/(4x+5))^2) ?
The derivative of ((2y+3/(4x+5))^2) is (2(2y+3)(2\frac{dy)/(dx)(4x+5)-4(2y+3))}{(4x+5)^3}
What is the first derivative of ((2y+3/(4x+5))^2) ?
The first derivative of ((2y+3/(4x+5))^2) is (2(2y+3)(2\frac{dy)/(dx)(4x+5)-4(2y+3))}{(4x+5)^3}