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Popular >

derivative of y=(2x-1)/(3x+5)

Solution

derivative of

y = \frac{2 x - 1}{3 x + 5}

Solution

\frac{13}{( 3 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 1}{3 x + 5})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (3 x + 5) = 3

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

Expand

2 (3 x + 5) - 3 (2 x - 1) : 13

= \frac{13}{( 3 x + 5 ) ^{2}}

Popular Examples

sum from n=1 to infinity of 6/((-5)^n)

n = 1 \sum \infty \frac{6}{( - 5 ) ^{n}}

y^{''}+256y=sec(16x),y(0)=-5,y^'(0)=-6

y^{^{''}} + 256 y = sec (16 x), y (0) = - 5, y^{^{'}} (0) = - 6

integral of (cos(5x))/(3+sin(5x))

\int \frac{cos ( 5 x )}{3 + sin ( 5 x )} d x

y^{''}+25y=5(csc(5t))^2

y^{^{''}} + 25 y = 5 (csc (5 t))^{2}

ty^'+(t+1)y=t,y(ln(6))=1

t y^{^{'}} + (t + 1) y = t, y (ln (6)) = 1

Frequently Asked Questions (FAQ)

What is the derivative of y=(2x-1)/(3x+5) ?
The derivative of y=(2x-1)/(3x+5) is (13)/((3x+5)^2)
What is the first derivative of y=(2x-1)/(3x+5) ?
The first derivative of y=(2x-1)/(3x+5) is (13)/((3x+5)^2)