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

The derivative of ((2x^2+3x))/(4x^2) is -3/(4x^2)

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

The first derivative of ((2x^2+3x))/(4x^2) is -3/(4x^2)

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derivative of

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

- \frac{3}{4 x ^{2}}

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{2 x ^{2} + 3 x}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 2 x ^{2} + 3 x ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 2 x ^{2} + 3 x )}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{4} \cdot \frac{( 4 x + 3 ) x ^{2} - 2 x ( 2 x ^{2} + 3 x )}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( 4 x + 3 ) x ^{2} - 2 x ( 2 x ^{2} + 3 x )}{( x ^{2} ) ^{2}} : - \frac{3}{4 x ^{2}}

= - \frac{3}{4 x ^{2}}

\frac{d}{d x} (a x sin (2 x) + b x cos (2 x))

\frac{d x}{d t} = - \frac{50}{π} x^{- \frac{3}{2}}

\int (sin (x) - 2 e^{x} + 3 x) d x

\int y^{2} (\frac{1}{y ^{5}} + \frac{y ^{4}}{2}) d y

6 x arcsin (x)

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