Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the derivative of the following function.

y=e^(-5x^(3))
Answer: 
y^(')=

Find the derivative of the following function.\newliney=e5x3 y=e^{-5 x^{3}} \newlineAnswer: y= y^{\prime}=

Full solution

Q. Find the derivative of the following function.\newliney=e5x3 y=e^{-5 x^{3}} \newlineAnswer: y= y^{\prime}=
  1. Identify Function & Rule: Identify the function and the rule to use for differentiation.\newlineWe have the function y=e5x3y=e^{-5x^{3}}. To find the derivative, we will use the chain rule, which 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.
  2. Apply Chain Rule: Apply the chain rule to differentiate the function.\newlineThe outer function is eue^u where u=5x3u=-5x^{3}. The derivative of eue^u with respect to uu is eue^u. The inner function is u=5x3u=-5x^{3}. The derivative of 5x3-5x^{3} with respect to xx is 15x2-15x^{2}.
  3. Multiply Derivatives: Multiply the derivatives of the outer and inner functions.\newlineUsing the chain rule, we multiply the derivative of the outer function by the derivative of the inner function to get the derivative of the composite function.\newliney=e5x3(15x2)y' = e^{-5x^{3}} \cdot (-15x^{2})
  4. Simplify Expression: Simplify the expression if possible.\newlineThe expression for the derivative is already simplified, so we can state the final answer.\newliney=15x2e5x3y' = -15x^{2}e^{-5x^{3}}

More problems from Find derivatives using logarithmic differentiation