Solve x^4-9x^3+15^2+93x-700

$$x ^ { 4 } - 9 x ^ { 3 } + 15 ^ { 2 } + 93 x - 700$$

Evaluate

$$x^{4}-9x^{3}+93x-475$$

Solution Steps

Calculate 15 to the power of 2 and get 225.

$$x^{4}-9x^{3}+225+93x-700$$

Subtract 700 from 225 to get -475.

$$x^{4}-9x^{3}-475+93x$$

Differentiate w.r.t. x

$$4x^{3}-27x^{2}+93$$

Steps Using Derivative Rule for Sum

Calculate 15 to the power of 2 and get 225.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-9x^{3}+225+93x-700)$$

Subtract 700 from 225 to get -475.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-9x^{3}-475+93x)$$

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}.

$$4x^{4-1}+3\left(-9\right)x^{3-1}+93x^{1-1}$$

Subtract 1 from 4.

$$4x^{3}+3\left(-9\right)x^{3-1}+93x^{1-1}$$

Multiply 3 times -9.

$$4x^{3}-27x^{3-1}+93x^{1-1}$$

Subtract 1 from 3.

$$4x^{3}-27x^{2}+93x^{1-1}$$

Subtract 1 from 1.

$$4x^{3}-27x^{2}+93x^{0}$$

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

$$4x^{3}-27x^{2}+93\times 1$$

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

$$4x^{3}-27x^{2}+93$$