Solve 4x^4-35x^3-7x^2+42

$$4 x ^ { 4 } - 35 x ^ { 3 } - 7 x ^ { 2 } + 42$$

Differentiate w.r.t. x

$$x\left(16x^{2}-105x-14\right)$$

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}.

$$4\times 4x^{4-1}+3\left(-35\right)x^{3-1}+2\left(-7\right)x^{2-1}$$

Multiply 4 times 4.

$$16x^{4-1}+3\left(-35\right)x^{3-1}+2\left(-7\right)x^{2-1}$$

Subtract 1 from 4.

$$16x^{3}+3\left(-35\right)x^{3-1}+2\left(-7\right)x^{2-1}$$

Multiply 3 times -35.

$$16x^{3}-105x^{3-1}+2\left(-7\right)x^{2-1}$$

Subtract 1 from 3.

$$16x^{3}-105x^{2}+2\left(-7\right)x^{2-1}$$

Multiply 3 times -35.

$$16x^{3}-105x^{2}-14x^{2-1}$$

Subtract 1 from 2.

$$16x^{3}-105x^{2}-14x^{1}$$

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

$$16x^{3}-105x^{2}-14x$$

Evaluate

$$4x^{4}-35x^{3}-7x^{2}+42$$