Solve 9x^2*3+6(9x^2)=

$$9 { x }^{ 2 } \times 3+6(9 { x }^{ 2 } )=$$

Evaluate

$$81x^{2}$$

Solution Steps

Multiply 9 and 3 to get 27.

$$27x^{2}+6\times 9x^{2}$$

Multiply 6 and 9 to get 54.

$$27x^{2}+54x^{2}$$

Combine 27x^{2} and 54x^{2} to get 81x^{2}.

$$81x^{2}$$

Differentiate w.r.t. x

$$162x$$

Steps Using Definition of a Derivative

Multiply 9 and 3 to get 27.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{2}+6\times 9x^{2})$$

Multiply 6 and 9 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27x^{2}+54x^{2})$$

Combine 27x^{2} and 54x^{2} to get 81x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(81x^{2})$$

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

$$2\times 81x^{2-1}$$

Multiply 2 times 81.

$$162x^{2-1}$$

Subtract 1 from 2.

$$162x^{1}$$

For any term t, t^{1}=t.

$$162x$$