Solve x+3x^2-4x+5x^3-10

$$x + 3 x ^ { 2 } - 4 x + 5 x ^ { 3 } - 10$$

Differentiate w.r.t. x

$$15x^{2}+6x-3$$

Steps Using Derivative Rule for Sum

Combine x and -4x to get -3x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-3x+3x^{2}+5x^{3}-10)$$

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}.

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

Subtract 1 from 1.

$$-3x^{0}+2\times 3x^{2-1}+3\times 5x^{3-1}$$

Multiply 2 times 3.

$$-3x^{0}+6x^{2-1}+3\times 5x^{3-1}$$

Subtract 1 from 2.

$$-3x^{0}+6x^{1}+3\times 5x^{3-1}$$

Multiply 2 times 3.

$$-3x^{0}+6x^{1}+15x^{3-1}$$

Subtract 1 from 3.

$$-3x^{0}+6x^{1}+15x^{2}$$

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

$$-3x^{0}+6x+15x^{2}$$

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

$$-3+6x+15x^{2}$$

Evaluate

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

Solution Steps

Combine x and -4x to get -3x.

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