Solve -2x^2*10x^4

$$- 2 x ^ { 2 } \cdot 10 x ^ { 4 }$$

Evaluate

$$-20x^{6}$$

Solution Steps

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

$$-2x^{6}\times 10$$

Multiply -2 and 10 to get -20.

$$-20x^{6}$$

Differentiate w.r.t. x

$$-120x^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{6}\times 10)$$

Multiply -2 and 10 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x^{6})$$

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

$$6\left(-20\right)x^{6-1}$$

Multiply 6 times -20.

$$-120x^{6-1}$$

Subtract 1 from 6.

$$-120x^{5}$$