Solve 30x^-2*-5x^-1

$$30 { x }^{ -2 } \times -5 { x }^{ -1 }$$

Evaluate

$$-\frac{150}{x^{3}}$$

Solution Steps

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

$$30x^{-3}\left(-5\right)$$

Multiply 30 and -5 to get -150.

$$-150x^{-3}$$

Differentiate w.r.t. x

$$\frac{450}{x^{4}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{-3}\left(-5\right))$$

Multiply 30 and -5 to get -150.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-150x^{-3})$$

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

$$-3\left(-150\right)x^{-3-1}$$

Multiply -3 times -150.

$$450x^{-3-1}$$

Subtract 1 from -3.

$$450x^{-4}$$