Solve x^12*x^7divx^3

$$x ^ { 12 } \times x ^ { 7 } \div x ^ { 3 }$$

Evaluate

$$x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 12 and 7 to get 19.

$$\frac{x^{19}}{x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 19 to get 16.

$$x^{16}$$

Differentiate w.r.t. x

$$16x^{15}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 12 and 7 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{19}}{x^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 19 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{16})$$

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

$$16x^{16-1}$$

Subtract 1 from 16.

$$16x^{15}$$