Find the derivative of the following function. y=e^(-6x^(6)-9x^(5)) Answer: y^(')=

Question

Find the derivative of the following function.  y=e^(-6x^(6)-9x^(5)) Answer:  y^(')=

Bytelearn · Accepted Answer

Identify function: Identify the function to differentiate. We are given the function y = e^(-6x^6 - 9x^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 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 e^u, where u = -6x^6 - 9x^5, and the inner function is u(x) = -6x^6 - 9x^5.Differentiate outer function: Differentiate the outer function with respect to the inner function. The derivative of e^u with respect to u is e^u. So, the derivative of e^(-6x^6 - 9x^5) with respect to the inner function u is e^(-6x^6 - 9x^5).Differentiate inner function: Differentiate the inner function with respect to x. The inner function u(x) = -6x^6 - 9x^5 is a polynomial, and we differentiate it term by term. The derivative of -6x^6 with respect to x is -36x^5, and the derivative of -9x^5 with respect to x is -45x^4.Combine using chain rule: Combine the results using the chain rule. Multiplying the derivative of the outer function by the derivative of the inner function, we get: y' = e^(-6x^6 - 9x^5) * (-36x^5 - 45x^4)Simplify expression: Simplify the expression if possible. In this case, there is no further simplification needed, so the final answer is: y' = e^(-6x^6 - 9x^5) * (-36x^5 - 45x^4)

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{6}-9 x^{5}}$ $\newline$ Answer: $y^{\prime}=$

Full solution

More problems from Find derivatives using logarithmic differentiation

Related topics

Find the derivative of the following function.\newliney=e−6x6−9x5 y=e^{-6 x^{6}-9 x^{5}} y=e−6x6−9x5\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=e^{-6 x^{6}-9 x^{5}}$ $\newline$ Answer: $y^{\prime}=$