Solve 3x*9x*2x^2=

$$3x \times 9x \times 2 { x }^{ 2 } =$$

Evaluate

$$54x^{4}$$

Solution Steps

Multiply x and x to get x^{2}.

$$3x^{2}\times 9\times 2x^{2}$$

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

$$3x^{4}\times 9\times 2$$

Multiply 3 and 9 to get 27.

$$27x^{4}\times 2$$

Multiply 27 and 2 to get 54.

$$54x^{4}$$

Differentiate w.r.t. x

$$216x^{3}$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}\times 9\times 2x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{4}\times 9\times 2)$$

Multiply 3 and 9 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{4}\times 2)$$

Multiply 27 and 2 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(54x^{4})$$

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

$$4\times 54x^{4-1}$$

Multiply 4 times 54.

$$216x^{4-1}$$

Subtract 1 from 4.

$$216x^{3}$$