Solve 2x^2*3x^-4

$$2 x ^ { 2 } \times 3 x ^ { - 4 }$$

Evaluate

$$\frac{6}{x^{2}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$2x^{-2}\times 3$$

Multiply 2 and 3 to get 6.

$$6x^{-2}$$

Differentiate w.r.t. x

$$-\frac{12}{x^{3}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-2}\times 3)$$

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{-2})$$

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

$$-2\times 6x^{-2-1}$$

Multiply -2 times 6.

$$-12x^{-2-1}$$

Subtract 1 from -2.

$$-12x^{-3}$$