Solve 8x^2*5x^2

$$8 { x }^{ 2 } \times 5 { x }^{ 2 }$$

Evaluate

$$40x^{4}$$

Solution Steps

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

$$8x^{4}\times 5$$

Multiply 8 and 5 to get 40.

$$40x^{4}$$

Differentiate w.r.t. x

$$160x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{4}\times 5)$$

Multiply 8 and 5 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}x}(40x^{4})$$

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

$$4\times 40x^{4-1}$$

Multiply 4 times 40.

$$160x^{4-1}$$

Subtract 1 from 4.

$$160x^{3}$$