Solve x^3*x^4*x*x

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

Evaluate

$$x^{9}$$

Solution Steps

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

$$x^{7}xx$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$x^{8}x$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$x^{9}$$

Differentiate w.r.t. x

$$9x^{8}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}x)$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{9})$$

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

$$9x^{9-1}$$

Subtract 1 from 9.

$$9x^{8}$$