Solve 10x-7+x^4+4x^3

$$10 x - 7 + x ^ { 4 } + 4 x ^ { 3 }$$

Differentiate w.r.t. x

$$4x^{3}+12x^{2}+10$$

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}.

$$10x^{1-1}+4x^{4-1}+3\times 4x^{3-1}$$

Subtract 1 from 1.

$$10x^{0}+4x^{4-1}+3\times 4x^{3-1}$$

Subtract 1 from 4.

$$10x^{0}+4x^{3}+3\times 4x^{3-1}$$

Multiply 4 times 1.

$$10x^{0}+4x^{3}+12x^{3-1}$$

Subtract 1 from 3.

$$10x^{0}+4x^{3}+12x^{2}$$

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

$$10\times 1+4x^{3}+12x^{2}$$

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

$$10+4x^{3}+12x^{2}$$

Evaluate

$$x^{4}+4x^{3}+10x-7$$