Solve 7x^3+2x^2-5x+6x^2-3+4x^3

$$7 x ^ { 3 } + 2 x ^ { 2 } - 5 x + 6 x ^ { 2 } - 3 + 4 x ^ { 3 }$$

Evaluate

$$11x^{3}+8x^{2}-5x-3$$

Solution Steps

Combine 2x^{2} and 6x^{2} to get 8x^{2}.

$$7x^{3}+8x^{2}-5x-3+4x^{3}$$

Combine 7x^{3} and 4x^{3} to get 11x^{3}.

$$11x^{3}+8x^{2}-5x-3$$

Differentiate w.r.t. x

$$33x^{2}+16x-5$$

Steps Using Derivative Rule for Sum

Combine 2x^{2} and 6x^{2} to get 8x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{3}+8x^{2}-5x-3+4x^{3})$$

Combine 7x^{3} and 4x^{3} to get 11x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}+8x^{2}-5x-3)$$

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}.

$$3\times 11x^{3-1}+2\times 8x^{2-1}-5x^{1-1}$$

Multiply 3 times 11.

$$33x^{3-1}+2\times 8x^{2-1}-5x^{1-1}$$

Subtract 1 from 3.

$$33x^{2}+2\times 8x^{2-1}-5x^{1-1}$$

Multiply 2 times 8.

$$33x^{2}+16x^{2-1}-5x^{1-1}$$

Subtract 1 from 2.

$$33x^{2}+16x^{1}-5x^{1-1}$$

Subtract 1 from 1.

$$33x^{2}+16x^{1}-5x^{0}$$

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

$$33x^{2}+16x-5x^{0}$$

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

$$33x^{2}+16x-5$$