Solve 5x^3*x^-2

$$5 x ^ { 3 } \times x ^ { - 2 }$$

Evaluate

$$5x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$5x^{1}$$

Calculate x to the power of 1 and get x.

$$5x$$

Differentiate w.r.t. x

$$5$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and -2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})$$

Calculate x to the power of 1 and get x.

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

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

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

Subtract 1 from 1.

$$5x^{0}$$

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

$$5\times 1$$

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

$$5$$