What is the derivative of (5x^3+9x^2)/x ?

The derivative of (5x^3+9x^2)/x is 10x+9

What is the first derivative of (5x^3+9x^2)/x ?

The first derivative of (5x^3+9x^2)/x is 10x+9

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derivative of

\frac{5 x ^{3} + 9 x ^{2}}{x}

10 x + 9

Solution steps

\frac{d}{d x} (\frac{5 x ^{3} + 9 x ^{2}}{x})

Simplify

\frac{5 x ^{3} + 9 x ^{2}}{x} : x (5 x + 9)

= \frac{d}{d x} (x (5 x + 9))

Apply the Product Rule:

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

f = x, g = 5 x + 9

= \frac{d x}{d x} (5 x + 9) + \frac{d}{d x} (5 x + 9) x

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

\frac{d}{d x} (5 x + 9) = 5

= 1 \cdot (5 x + 9) + 5 x

Simplify

= 10 x + 9

\int \frac{1}{5 cos ( x ) - 4} d x

\int x^{2} \cdot lo g_{e} (x) d x

x \to - 3 lim (- x^{2})

\frac{\partial}{\partial x} ((x + y + z)^{2})

\int_{0}^{4} t 16 - 3 t d t

What is the derivative of (5x^3+9x^2)/x ?
The derivative of (5x^3+9x^2)/x is 10x+9
What is the first derivative of (5x^3+9x^2)/x ?
The first derivative of (5x^3+9x^2)/x is 10x+9