What is the derivative of y=x(7x+3)^{1/3} ?

The derivative of y=x(7x+3)^{1/3} is (28x+9)/(3(7x+3)^{2/3)}

What is the first derivative of y=x(7x+3)^{1/3} ?

The first derivative of y=x(7x+3)^{1/3} is (28x+9)/(3(7x+3)^{2/3)}

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derivative of

y = x (7 x + 3)^{\frac{1}{3}}

\frac{28 x + 9}{3 ( 7 x + 3 ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d x} (x (7 x + 3)^{\frac{1}{3}})

Apply the Product Rule:

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

f = x, g = (7 x + 3)^{\frac{1}{3}}

= \frac{d x}{d x} (7 x + 3)^{\frac{1}{3}} + \frac{d}{d x} ((7 x + 3)^{\frac{1}{3}}) x

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

\frac{d}{d x} ((7 x + 3)^{\frac{1}{3}}) = \frac{7}{3 ( 7 x + 3 ) ^{\frac{2}{3}}}

= 1 \cdot (7 x + 3)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 3 ) ^{\frac{2}{3}}} x

Simplify

1 \cdot (7 x + 3)^{\frac{1}{3}} + \frac{7}{3 ( 7 x + 3 ) ^{\frac{2}{3}}} x : \frac{28 x + 9}{3 ( 7 x + 3 ) ^{\frac{2}{3}}}

= \frac{28 x + 9}{3 ( 7 x + 3 ) ^{\frac{2}{3}}}

What is the derivative of y=x(7x+3)^{1/3} ?
The derivative of y=x(7x+3)^{1/3} is (28x+9)/(3(7x+3)^{2/3)}
What is the first derivative of y=x(7x+3)^{1/3} ?
The first derivative of y=x(7x+3)^{1/3} is (28x+9)/(3(7x+3)^{2/3)}