Solve -100*0,002x^2*10*10

$$- 100 \cdot 0,002 x ^ { 2 } \cdot 10 \cdot 10$$

Evaluate

$$-20x^{2}$$

Solution Steps

Multiply -100 and 0,002 to get -0,2.

$$-0,2x^{2}\times 10\times 10$$

Multiply -0,2 and 10 to get -2.

$$-2x^{2}\times 10$$

Multiply -2 and 10 to get -20.

$$-20x^{2}$$

Differentiate w.r.t. x

$$-40x$$

Steps Using Definition of a Derivative

Multiply -100 and 0,002 to get -0,2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-0,2x^{2}\times 10\times 10)$$

Multiply -0,2 and 10 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{2}\times 10)$$

Multiply -2 and 10 to get -20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-20x^{2})$$

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

$$2\left(-20\right)x^{2-1}$$

Multiply 2 times -20.

$$-40x^{2-1}$$

Subtract 1 from 2.

$$-40x^{1}$$

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

$$-40x$$