Solve x^4-4x^3+10^2-17x

$$x ^ { 4 } - 4 x ^ { 3 } + 10 ^ { 2 } - 17 x$$

Differentiate w.r.t. x

$$4x^{3}-12x^{2}-17$$

Steps Using Derivative Rule for Sum

Calculate 10 to the power of 2 and get 100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-4x^{3}+100-17x)$$

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}.

$$4x^{4-1}+3\left(-4\right)x^{3-1}-17x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+3\left(-4\right)x^{3-1}-17x^{1-1}$$

Multiply 3 times -4.

$$4x^{3}-12x^{3-1}-17x^{1-1}$$

Subtract 1 from 3.

$$4x^{3}-12x^{2}-17x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-12x^{2}-17x^{0}$$

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

$$4x^{3}-12x^{2}-17$$

Evaluate

$$x^{4}-4x^{3}-17x+100$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$x^{4}-4x^{3}+100-17x$$