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

The derivative of (5x^2+3sqrt(x))/(2x) is (10x^2-3sqrt(x))/(4x^2)

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

The first derivative of (5x^2+3sqrt(x))/(2x) is (10x^2-3sqrt(x))/(4x^2)

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derivative of

\frac{5 x ^{2} + 3 x}{2 x}

\frac{10 x ^{2} - 3 x}{4 x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x^{2} + 3 x) = 10 x + \frac{3}{2 x}

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

= \frac{1}{2} \cdot \frac{( 10 x + \frac{3}{2 x} ) x - 1 \cdot ( 5 x ^{2} + 3 x )}{x ^{2}}

Simplify

\frac{1}{2} \cdot \frac{( 10 x + \frac{3}{2 x} ) x - 1 \cdot ( 5 x ^{2} + 3 x )}{x ^{2}} : \frac{10 x ^{2} - 3 x}{4 x ^{2}}

= \frac{10 x ^{2} - 3 x}{4 x ^{2}}

y = (x^{3} - 25 x)^{14}, (- 5, 0)

n = 0 \sum \infty \frac{1}{( n + 1 )}

n = 1 \sum \infty \frac{n !}{n 7 ^{n}}

f (x) = 2 cos (3 x), at x = \frac{π}{2}

What is the derivative of (5x^2+3sqrt(x))/(2x) ?
The derivative of (5x^2+3sqrt(x))/(2x) is (10x^2-3sqrt(x))/(4x^2)
What is the first derivative of (5x^2+3sqrt(x))/(2x) ?
The first derivative of (5x^2+3sqrt(x))/(2x) is (10x^2-3sqrt(x))/(4x^2)