What is (\partial)/(\partial x)(3/4 (2-3x)^{4/3}) ?

The answer to (\partial)/(\partial x)(3/4 (2-3x)^{4/3}) is -3(2-3x)^{1/3}

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(\partial)/(\partial x)(3/4 (2-3x)^{4/3})

\frac{\partial}{\partial x} (\frac{3}{4} (2 - 3 x)^{\frac{4}{3}})

- 3 (2 - 3 x)^{\frac{1}{3}}

Solution steps

\frac{\partial}{\partial x} (\frac{3}{4} (2 - 3 x)^{\frac{4}{3}})

Take the constant out:

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

= \frac{3}{4} \frac{\partial}{\partial x} ((2 - 3 x)^{\frac{4}{3}})

Apply the chain rule:

\frac{4 ( 2 - 3 x ) ^{\frac{1}{3}}}{3} \frac{\partial}{\partial x} (2 - 3 x)

= \frac{4 ( 2 - 3 x ) ^{\frac{1}{3}}}{3} \frac{\partial}{\partial x} (2 - 3 x)

\frac{\partial}{\partial x} (2 - 3 x) = - 3

= \frac{3}{4} \cdot \frac{4 ( 2 - 3 x ) ^{\frac{1}{3}}}{3} (- 3)

Simplify

\frac{3}{4} \cdot \frac{4 ( 2 - 3 x ) ^{\frac{1}{3}}}{3} (- 3) : - 3 (2 - 3 x)^{\frac{1}{3}}

= - 3 (2 - 3 x)^{\frac{1}{3}}

x \to 2 lim (2 x (x^{2} - 3))

\frac{d y}{d x} = \frac{e ^{x + y}}{y - 1}

y = 3 x^{2}, y = x^{4} - x^{2}

f (x) = 3 + 4 x^{2} - 2 x^{3}

\int \frac{1}{x ^{2} - y} d x

What is (\partial)/(\partial x)(3/4 (2-3x)^{4/3}) ?
The answer to (\partial)/(\partial x)(3/4 (2-3x)^{4/3}) is -3(2-3x)^{1/3}