Solve 45*122x*5x

$$45 \times 122x \times 5x$$

Evaluate

$$27450x^{2}$$

Solution Steps

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

$$45\times 122x^{2}\times 5$$

Multiply 45 and 122 to get 5490.

$$5490x^{2}\times 5$$

Multiply 5490 and 5 to get 27450.

$$27450x^{2}$$

Differentiate w.r.t. x

$$54900x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(45\times 122x^{2}\times 5)$$

Multiply 45 and 122 to get 5490.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5490x^{2}\times 5)$$

Multiply 5490 and 5 to get 27450.

$$\frac{\mathrm{d}}{\mathrm{d}x}(27450x^{2})$$

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

$$2\times 27450x^{2-1}$$

Multiply 2 times 27450.

$$54900x^{2-1}$$

Subtract 1 from 2.

$$54900x^{1}$$

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

$$54900x$$