Solve 1500*1275^2x

$$1500 \times 1275 ^ { 2 } x$$

Evaluate

$$2438437500x$$

Solution Steps

Calculate 1275 to the power of 2 and get 1625625.

$$1500\times 1625625x$$

Multiply 1500 and 1625625 to get 2438437500.

$$2438437500x$$

Differentiate w.r.t. x

$$2438437500$$

Steps Using Definition of a Derivative

Calculate 1275 to the power of 2 and get 1625625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(1500\times 1625625x)$$

Multiply 1500 and 1625625 to get 2438437500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2438437500x)$$

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

$$2438437500x^{1-1}$$

Subtract 1 from 1.

$$2438437500x^{0}$$

For any term t except 0, t^{0}=1.

$$2438437500\times 1$$

For any term t, t\times 1=t and 1t=t.

$$2438437500$$