f(x) = 15x^-2 - 9x^3, find the value of f'(-1), explaining how to find the derivative
To find the derivative of the function f(x) = 15x^-2 - 9x^3, we need to apply the power rule of differentiation.
First, rewrite the function in a more simplified form by moving x^-2 to the denominator:
f(x) = 15/x^2 - 9x^3
Now, differentiate each term separately:
f'(x) = d/dx (15/x^2) - d/dx (9x^3)
f'(x) = -30/x^3 - 27x^2
To find the value of f'(-1), substitute x = -1 into the derivative:
f'(-1) = -30/(-1)^3 - 27(-1)^2
f'(-1) = -30 - 27
f'(-1) = -57
Therefore, the value of f'(-1) is -57.