Solve 10^2*2x^2*1^0

$$10 ^ { 2 } \times 2 x ^ { 2 } \times 1 ^ { 0 }$$

Evaluate

$$200x^{2}$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$100\times 2x^{2}\times 1^{0}$$

Multiply 100 and 2 to get 200.

$$200x^{2}\times 1^{0}$$

Calculate 1 to the power of 0 and get 1.

$$200x^{2}\times 1$$

Multiply 200 and 1 to get 200.

$$200x^{2}$$

Differentiate w.r.t. x

$$400x$$

Steps Using Definition of a Derivative

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100\times 2x^{2}\times 1^{0})$$

Multiply 100 and 2 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(200x^{2}\times 1^{0})$$

Calculate 1 to the power of 0 and get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(200x^{2}\times 1)$$

Multiply 200 and 1 to get 200.

$$\frac{\mathrm{d}}{\mathrm{d}x}(200x^{2})$$

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

$$2\times 200x^{2-1}$$

Multiply 2 times 200.

$$400x^{2-1}$$

Subtract 1 from 2.

$$400x^{1}$$

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

$$400x$$