Solve (3110^2x^3-11x^2+36x-36

$$( 3110 ^ { 2 } x ^ { 3 } - 11 x ^ { 2 } + 36 x - 36$$

Differentiate w.r.t. x

$$29016300x^{2}-22x+36$$

Steps Using Derivative Rule for Sum

Calculate 3110 to the power of 2 and get 9672100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9672100x^{3}-11x^{2}+36x-36)$$

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}.

$$3\times 9672100x^{3-1}+2\left(-11\right)x^{2-1}+36x^{1-1}$$

Multiply 3 times 9672100.

$$29016300x^{3-1}+2\left(-11\right)x^{2-1}+36x^{1-1}$$

Subtract 1 from 3.

$$29016300x^{2}+2\left(-11\right)x^{2-1}+36x^{1-1}$$

Multiply 2 times -11.

$$29016300x^{2}-22x^{2-1}+36x^{1-1}$$

Subtract 1 from 2.

$$29016300x^{2}-22x^{1}+36x^{1-1}$$

Subtract 1 from 1.

$$29016300x^{2}-22x^{1}+36x^{0}$$

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

$$29016300x^{2}-22x+36x^{0}$$

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

$$29016300x^{2}-22x+36\times 1$$

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

$$29016300x^{2}-22x+36$$

Evaluate

$$9672100x^{3}-11x^{2}+36x-36$$

Solution Steps

Calculate 3110 to the power of 2 and get 9672100.

$$9672100x^{3}-11x^{2}+36x-36$$