Solve 27*4v9*3v9

$$27 \cdot 4 v 9 \cdot 3 v 9$$

Evaluate

$$324v_{9}^{2}$$

Solution Steps

Multiply v_{9} and v_{9} to get v_{9}^{2}.

$$27\times 4v_{9}^{2}\times 3$$

Multiply 27 and 4 to get 108.

$$108v_{9}^{2}\times 3$$

Multiply 108 and 3 to get 324.

$$324v_{9}^{2}$$

Differentiate w.r.t. v_9

$$648v_{9}$$

Steps Using Definition of a Derivative

Multiply v_{9} and v_{9} to get v_{9}^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}v_{9}}(27\times 4v_{9}^{2}\times 3)$$

Multiply 27 and 4 to get 108.

$$\frac{\mathrm{d}}{\mathrm{d}v_{9}}(108v_{9}^{2}\times 3)$$

Multiply 108 and 3 to get 324.

$$\frac{\mathrm{d}}{\mathrm{d}v_{9}}(324v_{9}^{2})$$

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

$$2\times 324v_{9}^{2-1}$$

Multiply 2 times 324.

$$648v_{9}^{2-1}$$

Subtract 1 from 2.

$$648v_{9}^{1}$$

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

$$648v_{9}$$