Question

Find $d y / d x$ $$y=\sqrt[4]{3 x^{2}-4 x}$$

   Find $d y / d x$
$$y=\sqrt[4]{3 x^{2}-4 x}$$

Calculus

Dale Varberg, Edwin… 9th Edition

Chapter 2, Problem 23

Instant Answer

Solved by Expert Nick Johnson

06/13/2021

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We can write the function as $y=(3x^2-4x)^{1/4}$. Show more…

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Find $d y / d x$ $$y=\sqrt[4]{3 x^{2}-4 x}$$

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Key Concepts

Chain Rule

The chain rule is a fundamental technique in differentiation used for finding the derivative of composite functions. It involves taking the derivative of the outer function with respect to the inner function and multiplying it by the derivative of the inner function. This rule is essential when the function to be differentiated is nested within another function.

Power Rule

The power rule is a basic method in calculus for differentiating functions of the form x^n, where n is a real number. According to this rule, the derivative of x^n is n*x^(n-1). This rule is easily extended to functions involving fractional exponents, making it useful for differentiating radical expressions.

Differentiation of Composite Functions

Differentiation of composite functions involves applying both the power rule and the chain rule. When a function is composed of an outer function and an inner function, the derivative is obtained by first differentiating the outer function with respect to the inner function, and then multiplying by the derivative of the inner function. This process is crucial for handling functions that are not directly expressed in their simplest form.

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