Solve xquad0quad5quad5quad10quad15

$$x \quad 0 \quad 5 \quad 5 \quad 10 \quad 15$$

Evaluate

$$3750x_{0}$$

Solution Steps

Multiply 5 and 5 to get 25.

$$x_{0}\times 25\times 10\times 15$$

Multiply 25 and 10 to get 250.

$$x_{0}\times 250\times 15$$

Multiply 250 and 15 to get 3750.

$$x_{0}\times 3750$$

Differentiate w.r.t. x_0

$$3750$$

Steps Using Definition of a Derivative

Multiply 5 and 5 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}x_{0}}(x_{0}\times 25\times 10\times 15)$$

Multiply 25 and 10 to get 250.

$$\frac{\mathrm{d}}{\mathrm{d}x_{0}}(x_{0}\times 250\times 15)$$

Multiply 250 and 15 to get 3750.

$$\frac{\mathrm{d}}{\mathrm{d}x_{0}}(x_{0}\times 3750)$$

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

$$3750x_{0}^{1-1}$$

Subtract 1 from 1.

$$3750x_{0}^{0}$$

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

$$3750\times 1$$

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

$$3750$$