Solve 3x^3x^-5^

$$3 { x }^{ 3 } { x }^{ { -5 }^{ } }$$

Evaluate

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

Solution Steps

Calculate -5 to the power of 1 and get -5.

$$3x^{3}x^{-5}$$

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$3x^{-2}$$

Differentiate w.r.t. x

$$-\frac{6}{x^{3}}$$

Steps Using Definition of a Derivative

Calculate -5 to the power of 1 and get -5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}x^{-5})$$

To multiply powers of the same base, add their exponents. Add 3 and -5 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{-2})$$

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

$$-2\times 3x^{-2-1}$$

Multiply -2 times 3.

$$-6x^{-2-1}$$

Subtract 1 from -2.

$$-6x^{-3}$$