What is the derivative of x(5x+3)^{1/3} ?

The derivative of x(5x+3)^{1/3} is (20x+9)/(3(5x+3)^{2/3)}

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

The first derivative of x(5x+3)^{1/3} is (20x+9)/(3(5x+3)^{2/3)}

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derivative of

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

\frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

Solution steps

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

Apply the Product Rule:

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

f = x, g = (5 x + 3)^{\frac{1}{3}}

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

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

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

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

Simplify

1 \cdot (5 x + 3)^{\frac{1}{3}} + \frac{5}{3 ( 5 x + 3 ) ^{\frac{2}{3}}} x : \frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

= \frac{20 x + 9}{3 ( 5 x + 3 ) ^{\frac{2}{3}}}

\int 8 (x + 1) I n (x + 1) d x

n = 0 \sum \infty z^{3 n}

x \to \infty lim (\frac{a _{n + 1}}{a _{n}})

\frac{d r}{d t} = \frac{1}{t + 1}, r (0) = 1

(1 + x^{2}) y^{^{'}} + 1 + 2 x y = 0

What is the derivative of x(5x+3)^{1/3} ?
The derivative of x(5x+3)^{1/3} is (20x+9)/(3(5x+3)^{2/3)}
What is the first derivative of x(5x+3)^{1/3} ?
The first derivative of x(5x+3)^{1/3} is (20x+9)/(3(5x+3)^{2/3)}