Solve 2x^-6(x^-3/x^-10)

$$2 x ^ { - 6 } ( x ^ { - 3 } / x ^ { - 10 } )$$

Evaluate

$$2x$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -10 from -3 to get 7.

$$2x^{-6}x^{7}$$

To multiply powers of the same base, add their exponents. Add -6 and 7 to get 1.

$$2x^{1}$$

Calculate x to the power of 1 and get x.

$$2x$$

Differentiate w.r.t. x

$$2$$

Steps Using Definition of a Derivative

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -10 from -3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{-6}x^{7})$$

To multiply powers of the same base, add their exponents. Add -6 and 7 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x)$$

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

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

Subtract 1 from 1.

$$2x^{0}$$

For any term t except 0, t^{0}=1.

$$2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2$$