Given the function f(x)=(6+10x^(3))(8x^(3)-10+8x), find f^(')(x) in any form. Answer: f^(')(x)=

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Given the function  f(x)=(6+10x^(3))(8x^(3)-10+8x), find  f^(')(x) in any form. Answer:  f^(')(x)=

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Product Rule Explanation: To find the derivative of the function f(x)=(6+10x^(3))(8x^(3)-10+8x), we will use the product rule. The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function.Denote Functions: Let's denote the first function as u(x) = 6+10x^(3) and the second function as v(x) = 8x^(3)-10+8x. We will find the derivatives of u(x) and v(x) separately.Derivative of u(x): The derivative of u(x) = 6+10x^(3) with respect to x is u'(x) = 0 + 30x^(2), since the derivative of a constant is 0 and the derivative of x^(3) is 3x^(2) multiplied by the coefficient 10.Derivative of v(x): The derivative of v(x) = 8x^(3)-10+8x with respect to x is v'(x) = 24x^(2) + 0 + 8, since the derivative of x^(3) is 3x^(2) multiplied by the coefficient 8, the derivative of a constant is 0, and the derivative of x is 1 multiplied by the coefficient 8.Apply Product Rule: Now we apply the product rule: f'(x) = u'(x)v(x) + u(x)v'(x). Substituting the derivatives we found, we get f'(x) = (30x^(2))(8x^(3)-10+8x) + (6+10x^(3))(24x^(2)+8).Expand Terms: We will now expand the terms: f'(x) = 240x^(5) - 300x^(2) + 240x^(3) + 144x^(2) + 240x^(5) + 80x.Combine Like Terms: Combine like terms to simplify the expression: f'(x) = 240x^(5) + 240x^(5) + 240x^(3) - 300x^(2) + 144x^(2) + 80x.Final Answer: After combining like terms, we get f'(x) = 480x^(5) + 240x^(3) - 156x^(2) + 80x.We have found the derivative of the function f(x) in its simplified form. The final answer is f'(x) = 480x^(5) + 240x^(3) - 156x^(2) + 80x.

Given the function $f(x)=\left(6+10 x^{3}\right)\left(8 x^{3}-10+8 x\right)$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$

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Given the function f(x)=(6+10x3)(8x3−10+8x) f(x)=\left(6+10 x^{3}\right)\left(8 x^{3}-10+8 x\right) f(x)=(6+10x3)(8x3−10+8x), find f′(x) f^{\prime}(x) f′(x) in any form.\newlineAnswer: f′(x)= f^{\prime}(x)= f′(x)=

Given the function $f(x)=\left(6+10 x^{3}\right)\left(8 x^{3}-10+8 x\right)$ , find $f^{\prime}(x)$ in any form. $\newline$ Answer: $f^{\prime}(x)=$