Solve 2*10d_{m}*2d_{m}

$$2 \cdot 10 d _ { m } \cdot 2 d _ { m }$$

Evaluate

$$40d_{m}^{2}$$

Solution Steps

Multiply d_{m} and d_{m} to get d_{m}^{2}.

$$2\times 10d_{m}^{2}\times 2$$

Multiply 2 and 10 to get 20.

$$20d_{m}^{2}\times 2$$

Multiply 20 and 2 to get 40.

$$40d_{m}^{2}$$

Differentiate w.r.t. d_m

$$80d_{m}$$

Steps Using Definition of a Derivative

Multiply d_{m} and d_{m} to get d_{m}^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}d_{m}}(2\times 10d_{m}^{2}\times 2)$$

Multiply 2 and 10 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}d_{m}}(20d_{m}^{2}\times 2)$$

Multiply 20 and 2 to get 40.

$$\frac{\mathrm{d}}{\mathrm{d}d_{m}}(40d_{m}^{2})$$

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

$$2\times 40d_{m}^{2-1}$$

Multiply 2 times 40.

$$80d_{m}^{2-1}$$

Subtract 1 from 2.

$$80d_{m}^{1}$$

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

$$80d_{m}$$