Solve -9x^45x^2

$$-9 { x }^{ 4 } 5 { x }^{ 2 }$$

Evaluate

$$-45x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$-9x^{6}\times 5$$

Multiply -9 and 5 to get -45.

$$-45x^{6}$$

Differentiate w.r.t. x

$$-270x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-9x^{6}\times 5)$$

Multiply -9 and 5 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-45x^{6})$$

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

$$6\left(-45\right)x^{6-1}$$

Multiply 6 times -45.

$$-270x^{6-1}$$

Subtract 1 from 6.

$$-270x^{5}$$