Solve 3x^-5*4x

$$3 x ^ { - 5 } \cdot 4 x$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and 1 to get -4.

$$3x^{-4}\times 4$$

Multiply 3 and 4 to get 12.

$$12x^{-4}$$

Differentiate w.r.t. x

$$-\frac{48}{x^{5}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -5 and 1 to get -4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{-4}\times 4)$$

Multiply 3 and 4 to get 12.

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

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

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

Multiply -4 times 12.

$$-48x^{-4-1}$$

Subtract 1 from -4.

$$-48x^{-5}$$