Answer :
The derivative of f(x)=-8x³-7x⁶ is f'(x) = -24x² - 42x⁵.
The derivative of f(x)=-8x³-7x⁶ is given by f'(x) = -24x² - 42x⁵.
Let's proceed with the solution by applying the power rule.
Power Rule: The power rule is one of the most straightforward differentiation rules to remember, and it applies when a variable is multiplied by a power, e.g., xn.
We can also apply the power rule to polynomials by multiplying each term by its derivative.Example: If f(x) = x², then f'(x) = 2x.
Similarly, if g(x) = x³, then g'(x) = 3x².
Now we can find the derivative of the function f(x) = -8x³ - 7x⁶ as follows:f(x) = -8x³ - 7x⁶
We will apply the power rule and differentiate each term separately.
The derivative of -8x³ is -24x², and the derivative of -7x⁶ is -42x⁵.
Thus, the derivative of f(x)=-8x³-7x⁶ is f'(x) = -24x² - 42x⁵.
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