Solve p^2+4p+3quad10.s^2-6s

$$p ^ { 2 } + 4 p + 3 \quad 10 . s ^ { 2 } - 6 s$$

Differentiate w.r.t. p

$$2\left(p+2\right)$$

Steps Using Derivative Rule for Sum

Multiply 3 and 10 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}p}(p^{2}+4p+30)$$

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}.

$$2p^{2-1}+4p^{1-1}$$

Subtract 1 from 2.

$$2p^{1}+4p^{1-1}$$

Subtract 1 from 1.

$$2p^{1}+4p^{0}$$

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

$$2p+4p^{0}$$

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

$$2p+4\times 1$$

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

$$2p+4$$

Evaluate

$$p^{2}+4p+30$$

Solution Steps

Multiply 3 and 10 to get 30.

$$p^{2}+4p+30$$