What is the derivative of f(x)=(3/4)x^{4/3} ?

The derivative of f(x)=(3/4)x^{4/3} is x^{1/3}

What is the first derivative of f(x)=(3/4)x^{4/3} ?

The first derivative of f(x)=(3/4)x^{4/3} is x^{1/3}

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derivative of

f (x) = (\frac{3}{4}) x^{\frac{4}{3}}

x^{\frac{1}{3}}

Solution steps

\frac{d}{d x} (\frac{3}{4} x^{\frac{4}{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{3}{4} \frac{d}{d x} (x^{\frac{4}{3}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{3}{4} \cdot \frac{4}{3} x^{\frac{4}{3} - 1}

Simplify

\frac{3}{4} \cdot \frac{4}{3} x^{\frac{4}{3} - 1} : x^{\frac{1}{3}}

= x^{\frac{1}{3}}

What is the derivative of f(x)=(3/4)x^{4/3} ?
The derivative of f(x)=(3/4)x^{4/3} is x^{1/3}
What is the first derivative of f(x)=(3/4)x^{4/3} ?
The first derivative of f(x)=(3/4)x^{4/3} is x^{1/3}