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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= \frac{20 x + 3}{3 ( 5 x + 1 ) ^{\frac{2}{3}}}

\frac{1}{x}, 1, 4

y = \frac{5 x}{1 + x ^{2}}

x \to \infty lim (12)

y = 4 x \cdot tan (x), at x = π

\int 4 sin (x) d x

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