Solve -4x^3*10x^8

$$- 4 x ^ { 3 } \times 10 x ^ { 8 }$$

Evaluate

$$-40x^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$-4x^{11}\times 10$$

Multiply -4 and 10 to get -40.

$$-40x^{11}$$

Differentiate w.r.t. x

$$-440x^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-4x^{11}\times 10)$$

Multiply -4 and 10 to get -40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-40x^{11})$$

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

$$11\left(-40\right)x^{11-1}$$

Multiply 11 times -40.

$$-440x^{11-1}$$

Subtract 1 from 11.

$$-440x^{10}$$