Solve x^4+5x^4+7x+12

$${ x }^{ 4 } +5 { x }^{ 4 } +7x+12$$

Differentiate w.r.t. x

$$24x^{3}+7$$

Steps Using Derivative Rule for Sum

Combine x^{4} and 5x^{4} to get 6x^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{4}+7x+12)$$

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}.

$$4\times 6x^{4-1}+7x^{1-1}$$

Multiply 4 times 6.

$$24x^{4-1}+7x^{1-1}$$

Subtract 1 from 4.

$$24x^{3}+7x^{1-1}$$

Subtract 1 from 1.

$$24x^{3}+7x^{0}$$

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

$$24x^{3}+7\times 1$$

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

$$24x^{3}+7$$

Evaluate

$$6x^{4}+7x+12$$

Solution Steps

Combine x^{4} and 5x^{4} to get 6x^{4}.

$$6x^{4}+7x+12$$