Find the derivative of the following function. y=ln(-2x^(5)+x^(4)) Answer: y^(')=

Question

Find the derivative of the following function.  y=ln(-2x^(5)+x^(4)) Answer:  y^(')=

Bytelearn · Accepted Answer

Identify function: Identify the function to differentiate. The function given is y = ln(-2x^5 + x^4). We need to find the derivative of this function 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 ln(u) and the inner function is u = -2x^5 + x^4.Differentiate outer function: Differentiate the outer function. The derivative of ln(u) with respect to u is 1/u. So, if y = ln(u), then dy/du = 1/u.Differentiate inner function: Differentiate the inner function. The inner function is u = -2x^5 + x^4. We need to find du/dx. du/dx = d/dx(-2x^5) + d/dx(x^4) du/dx = -10x^4 + 4x^3Apply chain rule: Apply the chain rule. Now we combine the derivatives from Step 3 and Step 4 using the chain rule. dy/dx = dy/du * du/dx dy/dx = (1/u) * (-10x^4 + 4x^3)Substitute back: Substitute the inner function back into the derivative. We substitute u = -2x^5 + x^4 back into the derivative we found in Step 5. dy/dx = (1/(-2x^5 + x^4)) * (-10x^4 + 4x^3)Simplify expression: Simplify the expression. We can now simplify the expression to find the final derivative. dy/dx = (-10x^4 + 4x^3) / (-2x^5 + x^4)

Find the derivative of the following function. $\newline$ $y=\ln \left(-2 x^{5}+x^{4}\right)$ $\newline$ Answer: $y^{\prime}=$

Full solution

More problems from Find derivatives of radical functions

Related topics

Find the derivative of the following function.\newliney=ln⁡(−2x5+x4) y=\ln \left(-2 x^{5}+x^{4}\right) y=ln(−2x5+x4)\newlineAnswer: y′= y^{\prime}= y′=

Find the derivative of the following function. $\newline$ $y=\ln \left(-2 x^{5}+x^{4}\right)$ $\newline$ Answer: $y^{\prime}=$