Solve 24x^-3+1/-3+1

$$\frac{ 24 { x }^{ -3+1 } }{ -3+1 }$$

Evaluate

$$-\frac{12}{x^{2}}$$

Solution Steps

Add -3 and 1 to get -2.

$$\frac{24x^{-2}}{-3+1}$$

Add -3 and 1 to get -2.

$$\frac{24x^{-2}}{-2}$$

Divide 24x^{-2} by -2 to get -12x^{-2}.

$$-12x^{-2}$$

Differentiate w.r.t. x

$$\frac{24}{x^{3}}$$

Steps Using Definition of a Derivative

Add -3 and 1 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x^{-2}}{-3+1})$$

Add -3 and 1 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24x^{-2}}{-2})$$

Divide 24x^{-2} by -2 to get -12x^{-2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-12x^{-2})$$

The derivative of ax^{n} is nax^{n-1}.

$$-2\left(-12\right)x^{-2-1}$$

Multiply -2 times -12.

$$24x^{-2-1}$$

Subtract 1 from -2.

$$24x^{-3}$$