Question

Find the derivative of x⁵ - 4x³ + 2x³ - 10 with respect to x.

Answer 1

The derivative of the polynomial function x⁵ - 4x³ + 2x³ - 10 with respect to x, after simplifying, is 5x⁴ - 6x².

Step-by-step explanation:

To find the derivative of the polynomial function x⁵ - 4x³ + 2x³ - 10 with respect to x, we first simplify the function by combining like terms and then apply the power rule for differentiation.

The simplified function is:

x⁵ - 2x³ - 10.

Now, taking the derivative term by term:

• The derivative of x⁵ with respect to x is 5x⁴.
• The derivative of -2x³ with respect to x is -6x².
• And the derivative of the constant -10 is 0.

Therefore, the derivative of the function with respect to x is:

5x⁴ - 6x².