Question

Find the derivative of g(x) = (3 + 5x)⁵(3 - x⁴).

Answer 1

To find the derivative of g(x) = (3 + 5x)⁵(3 - x⁴), we can apply the product rule and the chain rule.

Step-by-step explanation:

To find the derivative of g(x) = (3 + 5x)⁵(3 - x⁴), we can use the product rule and the chain rule.

First, let's find the derivative of (3 + 5x)⁵:

• Let u = 3 + 5x
• Now, apply the chain rule: (d/dx) (u⁵) = 5u⁴ (du/dx)
• Substituting u back, we have: 5(3 + 5x)⁴(5)

Next, let's find the derivative of (3 - x⁴):

• The derivative of 3 is 0
• The derivative of -x⁴ is -4x³

Finally, we multiply these derivatives together:

g'(x) = (5(3 + 5x)⁴)(5) + 0(3 - x⁴) + (3 + 5x)⁵(-4x³)