Solve 5x^2*.5x^2

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

Evaluate

$$\frac{5x^{4}}{2}$$

Solution Steps

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

$$5x^{4}\times 0.5$$

Multiply 5 and 0.5 to get 2.5.

$$2.5x^{4}$$

Differentiate w.r.t. x

$$10x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{4}\times 0.5)$$

Multiply 5 and 0.5 to get 2.5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2.5x^{4})$$

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

$$4\times 2.5x^{4-1}$$

Multiply 4 times 2.5.

$$10x^{4-1}$$

Subtract 1 from 4.

$$10x^{3}$$