Solve 2x^6*3x^-9

$$2 x ^ { 6 } \times 3 x ^ { - 9 }$$

Evaluate

$$\frac{6}{x^{3}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and -9 to get -3.

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

Multiply 2 and 3 to get 6.

$$6x^{-3}$$

Differentiate w.r.t. x

$$-\frac{18}{x^{4}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and -9 to get -3.

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

Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{-3})$$

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

$$-3\times 6x^{-3-1}$$

Multiply -3 times 6.

$$-18x^{-3-1}$$

Subtract 1 from -3.

$$-18x^{-4}$$