Solve 56x^-4div14x^-8

$$56 x ^ { - 4 } \div 14 x ^ { - 8 }$$

Evaluate

$$\frac{4}{x^{12}}$$

Solution Steps

Divide 56x^{-4} by 14 to get 4x^{-4}.

$$4x^{-4}x^{-8}$$

To multiply powers of the same base, add their exponents. Add -4 and -8 to get -12.

$$4x^{-12}$$

Differentiate w.r.t. x

$$-\frac{48}{x^{13}}$$

Steps Using Definition of a Derivative

Divide 56x^{-4} by 14 to get 4x^{-4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-4}x^{-8})$$

To multiply powers of the same base, add their exponents. Add -4 and -8 to get -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{-12})$$

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

$$-12\times 4x^{-12-1}$$

Multiply -12 times 4.

$$-48x^{-12-1}$$

Subtract 1 from -12.

$$-48x^{-13}$$