Solve p^2-2pg+9^2=

$$p ^ { 2 } - 2 p g + 9 ^ { 2 } =$$

Differentiate w.r.t. p

$$2\left(p-g\right)$$

Steps Using Derivative Rule for Sum

Calculate 9 to the power of 2 and get 81.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{2}-2pg+81)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2p^{2-1}+\left(-2g\right)p^{1-1}$$

Subtract 1 from 2.

$$2p^{1}+\left(-2g\right)p^{1-1}$$

Subtract 1 from 1.

$$2p^{1}+\left(-2g\right)p^{0}$$

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

$$2p+\left(-2g\right)p^{0}$$

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

$$2p+\left(-2g\right)\times 1$$

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

$$2p-2g$$

Evaluate

$$p^{2}-2gp+81$$

Solution Steps

Calculate 9 to the power of 2 and get 81.

$$p^{2}-2pg+81$$