Let h(x)=sqrt(x^(5)). h^(')(4)=

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Let  h(x)=sqrt(x^(5)).  h^(')(4)=

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Rewrite function: To find the derivative of the function h(x) = sqrt(x^5), we first need to rewrite the function in a form that makes it easier to differentiate. The square root of x^5 can be written as (x^5)^(1/2).Apply chain rule: Now we apply the chain rule to differentiate the function. 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 u^(1/2) and the inner function is x^5.Differentiate outer function: Differentiating the outer function u^(1/2) with respect to u gives (1/2)u^(-1/2). Then we differentiate the inner function x^5 with respect to x, which gives us 5x^4.Combine derivatives: Now we combine the derivatives of the outer and inner functions. The derivative of h(x) is (1/2)(x^5)^(-1/2) * 5x^4.Simplify expression: Simplify the expression by combining like terms. This gives us (5/2)x^(4 - 1/2), which simplifies to (5/2)x^(7/2).Evaluate at x=4: Now we evaluate the derivative at x = 4. We substitute x with 4 in the expression (5/2)x^(7/2) to get (5/2)(4)^(7/2).Calculate value: Calculate the value of (4)^(7/2). Since (4)^(7/2) is the same as sqrt(4^7), and 4^7 is 16384, we take the square root of 16384, which is 128.Multiply to get final answer: Now multiply (5/2) by 128 to get the final answer. (5/2) * 128 = 5 * 64 = 320.

Let $h(x)=\sqrt{x^{5}}$ . $\newline$ $h^{\prime}(4)=$

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Let h(x)=x5 h(x)=\sqrt{x^{5}} h(x)=x5​.\newlineh′(4)= h^{\prime}(4)= h′(4)=

Let $h(x)=\sqrt{x^{5}}$ . $\newline$ $h^{\prime}(4)=$