Solve 9x^2(4x^2)2

$$9 { x }^{ 2 } (4 { x }^{ 2 } )2$$

Evaluate

$$72x^{4}$$

Solution Steps

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

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

Multiply 9 and 4 to get 36.

$$36x^{4}\times 2$$

Multiply 36 and 2 to get 72.

$$72x^{4}$$

Differentiate w.r.t. x

$$288x^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 9 and 4 to get 36.

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{4}\times 2)$$

Multiply 36 and 2 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}x}(72x^{4})$$

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

$$4\times 72x^{4-1}$$

Multiply 4 times 72.

$$288x^{4-1}$$

Subtract 1 from 4.

$$288x^{3}$$