Solve 2x^3-15x+36x-10

$$2 { x }^{ 3 } -15x+36x-10$$

Differentiate w.r.t. x

$$6x^{2}+21$$

Steps Using Derivative Rule for Sum

Combine -15x and 36x to get 21x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+21x-10)$$

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}.

$$3\times 2x^{3-1}+21x^{1-1}$$

Multiply 3 times 2.

$$6x^{3-1}+21x^{1-1}$$

Subtract 1 from 3.

$$6x^{2}+21x^{1-1}$$

Subtract 1 from 1.

$$6x^{2}+21x^{0}$$

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

$$6x^{2}+21\times 1$$

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

$$6x^{2}+21$$

Evaluate

$$2x^{3}+21x-10$$

Solution Steps

Combine -15x and 36x to get 21x.

$$2x^{3}+21x-10$$