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Find the derivative of the following function.

y=e^(2x^(6)+2x^(5))
Answer:
y^(')=

Find the derivative of the following function. $\newline$ $y=e^{2 x^{6}+2 x^{5}}$ $\newline$ Answer: $y^{\prime}=$

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Find derivatives using logarithmic differentiation

Full solution

Q. Find the derivative of the following function.

\newline

y=e^{2 x^{6}+2 x^{5}}

\newline

Answer:

y^{\prime}=

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $y=e^{2x^{6}+2x^{5}}$ . We need to find its derivative with respect to $x$ .
Apply Chain Rule: Apply the chain rule for differentiation. The chain rule states that the derivative of $e^u$ , where $u$ is a function of $x$ , is $e^u$ times the derivative of $u$ with respect to $x$ . In this case, $u = 2x^6 + 2x^5$ .
Differentiate Inner Function: Differentiate the inner function $u = 2x^6 + 2x^5$ with respect to $x$ . The derivative of $2x^6$ with respect to $x$ is $12x^5$ , and the derivative of $2x^5$ with respect to $x$ is $10x^4$ . So, the derivative of $u$ with respect to $x$ is $x$ $0$ .
Multiply by $e^u$ : Multiply the derivative of the inner function by $e^u$ to get the derivative of $y$ . Using the chain rule from Step $2$ , we multiply $e^{(2x^6 + 2x^5)}$ by the derivative of the inner function $(12x^5 + 10x^4)$ to get the derivative of $y$ . $y' = e^{(2x^6 + 2x^5)} \cdot (12x^5 + 10x^4)$
Simplify Expression: Simplify the expression if possible. $\newline$ In this case, the expression is already simplified, so we can state the final answer. $\newline$ $y' = e^{2x^6 + 2x^5} \cdot (12x^5 + 10x^4)$

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