Solve 7P(1)+3P(-2)=?

$$7 P ( 1 ) + 3 P ( - 2 ) = ?$$

Evaluate

$$P$$

Solution Steps

Multiply 7 and 1 to get 7.

$$7P+3P\left(-2\right)$$

Multiply 3 and -2 to get -6.

$$7P-6P$$

Combine 7P and -6P to get P.

$$P$$

Differentiate w.r.t. P

$$1$$

Steps Using Definition of a Derivative

Multiply 7 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}P}(7P+3P\left(-2\right))$$

Multiply 3 and -2 to get -6.

$$\frac{\mathrm{d}}{\mathrm{d}P}(7P-6P)$$

Combine 7P and -6P to get P.

$$\frac{\mathrm{d}}{\mathrm{d}P}(P)$$

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

$$P^{1-1}$$

Subtract 1 from 1.

$$P^{0}$$

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

$$1$$