Solve 6P^2-4P+9-4P^2+7P-4

$$6 P ^ { 2 } - 4 P + 9 - 4 P ^ { 2 } + 7 P - 4$$

Evaluate

$$2P^{2}+3P+5$$

Solution Steps

Combine 6P^{2} and -4P^{2} to get 2P^{2}.

$$2P^{2}-4P+9+7P-4$$

Combine -4P and 7P to get 3P.

$$2P^{2}+3P+9-4$$

Subtract 4 from 9 to get 5.

$$2P^{2}+3P+5$$

Differentiate w.r.t. P

$$4P+3$$

Steps Using Derivative Rule for Sum

Combine 6P^{2} and -4P^{2} to get 2P^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}P}(2P^{2}-4P+9+7P-4)$$

Combine -4P and 7P to get 3P.

$$\frac{\mathrm{d}}{\mathrm{d}P}(2P^{2}+3P+9-4)$$

Subtract 4 from 9 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}P}(2P^{2}+3P+5)$$

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}.

$$2\times 2P^{2-1}+3P^{1-1}$$

Multiply 2 times 2.

$$4P^{2-1}+3P^{1-1}$$

Subtract 1 from 2.

$$4P^{1}+3P^{1-1}$$

Subtract 1 from 1.

$$4P^{1}+3P^{0}$$

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

$$4P+3P^{0}$$

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

$$4P+3\times 1$$

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

$$4P+3$$