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

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

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

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

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\frac{d}{d x} (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}}}

1 1^{x}

y = (2 x - 3) (x + 3)^{3}

y^{^{'}} = y (x y^{3} + 2)

\int e^{3 x} e^{x} d x

\frac{d}{d x} (- sin (x) - 1)

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