Let g(x)=root(3)(x^(4)). g^(')(x)=

Question

Let  g(x)=root(3)(x^(4)).  g^(')(x)=

Bytelearn · Accepted Answer

Apply Chain Rule: To find the derivative of the function g(x) = ∛(x⁴), we will use the chain rule. The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is the cube root function, and the inner function is x⁴.Rewrite Function: First, let's write the function in a form that makes it easier to differentiate. The cube root of x⁴ can be written as (x⁴)^(1/3).Differentiate with Power Rule: Now, we differentiate (x⁴)^(1/3) with respect to x. Using the power rule, which states that the derivative of x^n with respect to x is n*x^(n-1), we get: g'(x) = (1/3)*(x⁴)^((1/3)-1) = (1/3)*(x⁴)^(-2/3).Simplify Expression: Next, we simplify the expression. We can rewrite (x⁴)^(-2/3) as 1/(x⁴)^(2/3), which is the same as 1/(x^(8/3)). So, we have: g'(x) = (1/3) * (1/(x^(8/3))).Combine Constants and Terms: Finally, we can simplify the expression further by combining the constants and the x terms: g'(x) = 1/(3*x^(8/3)).

Let $g(x)=\sqrt[3]{x^{4}}$ . $\newline$ $g^{\prime}(x)=$

Full solution

More problems from Simplify variable expressions using properties

Related topics

Let g(x)=x43 g(x)=\sqrt[3]{x^{4}} g(x)=3x4​.\newlineg′(x)= g^{\prime}(x)= g′(x)=

Let $g(x)=\sqrt[3]{x^{4}}$ . $\newline$ $g^{\prime}(x)=$