Solve 9/4x^2*2x^2

$$\frac{ 9 }{ 4 } { x }^{ 2 } \times 2 { x }^{ 2 }$$

Evaluate

$$\frac{9x^{4}}{2}$$

Solution Steps

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

$$\frac{9}{4}x^{4}\times 2$$

Multiply \frac{9}{4} and 2 to get \frac{9}{2}.

$$\frac{9}{2}x^{4}$$

Differentiate w.r.t. x

$$18x^{3}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{4}x^{4}\times 2)$$

Multiply \frac{9}{4} and 2 to get \frac{9}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{2}x^{4})$$

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

$$4\times \frac{9}{2}x^{4-1}$$

Multiply 4 times \frac{9}{2}.

$$18x^{4-1}$$

Subtract 1 from 4.

$$18x^{3}$$