Solve x^3*x^4/x^2

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

Evaluate

$$x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{7}}{x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 7 to get 5.

$$x^{5}$$

Differentiate w.r.t. x

$$5x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 7 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5})$$

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

$$5x^{5-1}$$

Subtract 1 from 5.

$$5x^{4}$$