Solve 5x^3-8x^2+30x-20

$$5 { x }^{ 3 } -8 { x }^{ 2 } +30x-20$$

Differentiate w.r.t. x

$$15x^{2}-16x+30$$

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}.

$$3\times 5x^{3-1}+2\left(-8\right)x^{2-1}+30x^{1-1}$$

Multiply 3 times 5.

$$15x^{3-1}+2\left(-8\right)x^{2-1}+30x^{1-1}$$

Subtract 1 from 3.

$$15x^{2}+2\left(-8\right)x^{2-1}+30x^{1-1}$$

Multiply 2 times -8.

$$15x^{2}-16x^{2-1}+30x^{1-1}$$

Subtract 1 from 2.

$$15x^{2}-16x^{1}+30x^{1-1}$$

Subtract 1 from 1.

$$15x^{2}-16x^{1}+30x^{0}$$

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

$$15x^{2}-16x+30x^{0}$$

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

$$15x^{2}-16x+30\times 1$$

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

$$15x^{2}-16x+30$$

Evaluate

$$5x^{3}-8x^{2}+30x-20$$