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

The derivative of (5x^3+5x^2/x) is 5(2x+1)

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

The first derivative of (5x^3+5x^2/x) is 5(2x+1)

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

5 (2 x + 1)

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x + 1

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

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

\frac{d}{d x} (x + 1) = 1

= 5 (1 \cdot (x + 1) + 1 \cdot x)

Simplify

5 (1 \cdot (x + 1) + 1 \cdot x) : 5 (2 x + 1)

= 5 (2 x + 1)

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