Solve 2x^3*2x^2=

$$2 x ^ { 3 } \cdot 2 x ^ { 2 } =$$

Evaluate

$$4x^{5}$$

Solution Steps

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

$$2x^{5}\times 2$$

Multiply 2 and 2 to get 4.

$$4x^{5}$$

Differentiate w.r.t. x

$$20x^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{5}\times 2)$$

Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{5})$$

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

$$5\times 4x^{5-1}$$

Multiply 5 times 4.

$$20x^{5-1}$$

Subtract 1 from 5.

$$20x^{4}$$