Solve +12x^4+19x^4+21x^2+13x+3

$$+ 12 x ^ { 4 } + 19 x ^ { 4 } + 21 x ^ { 2 } + 13 x + 3$$

Differentiate w.r.t. x

$$124x^{3}+42x+13$$

Steps Using Derivative Rule for Sum

Combine 12x^{4} and 19x^{4} to get 31x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(31x^{4}+21x^{2}+13x+3)$$

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}.

$$4\times 31x^{4-1}+2\times 21x^{2-1}+13x^{1-1}$$

Multiply 4 times 31.

$$124x^{4-1}+2\times 21x^{2-1}+13x^{1-1}$$

Subtract 1 from 4.

$$124x^{3}+2\times 21x^{2-1}+13x^{1-1}$$

Multiply 2 times 21.

$$124x^{3}+42x^{2-1}+13x^{1-1}$$

Subtract 1 from 2.

$$124x^{3}+42x^{1}+13x^{1-1}$$

Subtract 1 from 1.

$$124x^{3}+42x^{1}+13x^{0}$$

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

$$124x^{3}+42x+13x^{0}$$

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

$$124x^{3}+42x+13\times 1$$

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

$$124x^{3}+42x+13$$

Evaluate

$$31x^{4}+21x^{2}+13x+3$$

Solution Steps

Combine 12x^{4} and 19x^{4} to get 31x^{4}.

$$31x^{4}+21x^{2}+13x+3$$