Solve 5x^3+2x^2+1-7x+10

$$5 x ^ { 3 } + 2 x ^ { 2 } + 1 - 7 x + 10$$

Differentiate w.r.t. x

$$15x^{2}+4x-7$$

Steps Using Derivative Rule for Sum

Add 1 and 10 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+2x^{2}+11-7x)$$

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}.

$$3\times 5x^{3-1}+2\times 2x^{2-1}-7x^{1-1}$$

Multiply 3 times 5.

$$15x^{3-1}+2\times 2x^{2-1}-7x^{1-1}$$

Subtract 1 from 3.

$$15x^{2}+2\times 2x^{2-1}-7x^{1-1}$$

Multiply 2 times 2.

$$15x^{2}+4x^{2-1}-7x^{1-1}$$

Subtract 1 from 2.

$$15x^{2}+4x^{1}-7x^{1-1}$$

Subtract 1 from 1.

$$15x^{2}+4x^{1}-7x^{0}$$

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

$$15x^{2}+4x-7x^{0}$$

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

$$15x^{2}+4x-7$$

Evaluate

$$5x^{3}+2x^{2}-7x+11$$

Solution Steps

Add 1 and 10 to get 11.

$$5x^{3}+2x^{2}+11-7x$$