Question

Find the derivative of the function: y = (8x⁴ - 7x² + 7⁴).

Answer 1

The derivative of the function y = (8x⁴ - 7x² + 7⁴) is found using the power rule to be 32x^3 - 14x.

Step-by-step explanation:

To find the derivative of the function y = (8x⁴ - 7x² + 7⁴), we can apply the power rule of differentiation. The power rule states that if f(x) = ax^n, then f'(x) = n*ax^(n-1). Applying this rule to each term of the function:

• The derivative of 8x4 is 8 * 4x3 or 32x3.
• The derivative of -7x2 is -7 * 2x or -14x.
• The derivative of a constant like 74 is 0 since the derivative of any constant is 0.

Putting it all together, the derivative of the function y is thus 32x3 - 14x.