Solve x^4+x^3+7^2+x

$$x ^ { 4 } + x ^ { 3 } + 7 ^ { 2 } + x$$

Differentiate w.r.t. x

$$4x^{3}+3x^{2}+1$$

Steps Using Derivative Rule for Sum

Calculate 7 to the power of 2 and get 49.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}+x^{3}+49+x)$$

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}.

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

Subtract 1 from 4.

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

Subtract 1 from 3.

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

Subtract 1 from 1.

$$4x^{3}+3x^{2}+x^{0}$$

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

$$4x^{3}+3x^{2}+1$$

Evaluate

$$x^{4}+x^{3}+x+49$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

$$x^{4}+x^{3}+49+x$$