How do you find the derivative of f(x)=-2x^-3+x^2-7?

2 Answers
Jul 29, 2018

f'(x)=6x^-4+2x

Explanation:

Use the power rule for differentiation:

We know that the derivative of x^n is nx^(n-1).

The function f(x)=-2x^(-3)+x^2-7 has three parts.

We apply the power rule on each part.

color(red)(Part-1: -2x^-3
Derivative: -2(-3)x^((-3-1))
Derivative: color(red)(6x^-4

color(blue)(Part-2: x^2
Derivative: (2)x^((2-1))
Derivative: color(blue)(2x

color(green)(Part-3: 7
The derivative of a constant is zero, so:
Derivative: color(green)(0

We add the derivatives of each part up:

color(red)(6x^-4)+color(blue)(2x)+color(green)(0)

So the derivative would be:

f'(x)=6x^-4+2x

Jul 29, 2018

6x^(-4)+2x

Explanation:

Since we're dealing with a polynomial, we can find the derivative with the help of the Power Rule.

We simply multiply the exponent by the coefficient, and decrement the power by one. Recall that the derivative of a constant is zero.

We now have:

6x^(-4)+2x

Hope this helps!