Solve (14p^4+11p^2-9p^3)-(-14

$$( 14 p ^ { 4 } + 11 p ^ { 2 } - 9 p ^ { 3 } ) - ( - 14$$

Differentiate w.r.t. p

$$p\left(56p^{2}-27p+22\right)$$

Steps Using Derivative Rule for Sum

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}.

$$4\times 14p^{4-1}+2\times 11p^{2-1}+3\left(-9\right)p^{3-1}$$

Multiply 4 times 14.

$$56p^{4-1}+2\times 11p^{2-1}+3\left(-9\right)p^{3-1}$$

Subtract 1 from 4.

$$56p^{3}+2\times 11p^{2-1}+3\left(-9\right)p^{3-1}$$

Multiply 2 times 11.

$$56p^{3}+22p^{2-1}+3\left(-9\right)p^{3-1}$$

Subtract 1 from 2.

$$56p^{3}+22p^{1}+3\left(-9\right)p^{3-1}$$

Multiply 2 times 11.

$$56p^{3}+22p^{1}-27p^{3-1}$$

Subtract 1 from 3.

$$56p^{3}+22p^{1}-27p^{2}$$

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

$$56p^{3}+22p-27p^{2}$$

Evaluate

$$14p^{4}-9p^{3}+11p^{2}+14$$

Solution Steps

The opposite of -14 is 14.

$$14p^{4}+11p^{2}-9p^{3}+14$$