What is the derivative of (7x^2+5sqrt(x))/(4x) ?

The derivative of (7x^2+5sqrt(x))/(4x) is (14x^2-5sqrt(x))/(8x^2)

What is the first derivative of (7x^2+5sqrt(x))/(4x) ?

The first derivative of (7x^2+5sqrt(x))/(4x) is (14x^2-5sqrt(x))/(8x^2)

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derivative of

\frac{7 x ^{2} + 5 x}{4 x}

\frac{14 x ^{2} - 5 x}{8 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{7 x ^{2} + 5 x}{4 x})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{7 x ^{2} + 5 x}{x})

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} ( 7 x ^{2} + 5 x ) x - \frac{d x}{d x} ( 7 x ^{2} + 5 x )}{x ^{2}}

\frac{d}{d x} (7 x^{2} + 5 x) = 14 x + \frac{5}{2 x}

\frac{d x}{d x} = 1

= \frac{1}{4} \cdot \frac{( 14 x + \frac{5}{2 x} ) x - 1 \cdot ( 7 x ^{2} + 5 x )}{x ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( 14 x + \frac{5}{2 x} ) x - 1 \cdot ( 7 x ^{2} + 5 x )}{x ^{2}} : \frac{14 x ^{2} - 5 x}{8 x ^{2}}

= \frac{14 x ^{2} - 5 x}{8 x ^{2}}

\int \frac{lo g _{9} ( x )}{x} d x

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

\frac{\partial}{\partial x} (81 x^{8} y^{8} - 64 x^{7} y^{7})

\int_{0}^{\frac{π}{2}} x cos (x^{2}) d x

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

What is the derivative of (7x^2+5sqrt(x))/(4x) ?
The derivative of (7x^2+5sqrt(x))/(4x) is (14x^2-5sqrt(x))/(8x^2)
What is the first derivative of (7x^2+5sqrt(x))/(4x) ?
The first derivative of (7x^2+5sqrt(x))/(4x) is (14x^2-5sqrt(x))/(8x^2)