Solve 3x^3+8x-4x^5+6x+2+3

$$3 x ^ { 3 } + 8 x - 4 x ^ { 5 } + 6 x + 2 + 3$$

Evaluate

$$5+14x+3x^{3}-4x^{5}$$

Solution Steps

Combine 8x and 6x to get 14x.

$$3x^{3}+14x-4x^{5}+2+3$$

Add 2 and 3 to get 5.

$$3x^{3}+14x-4x^{5}+5$$

Differentiate w.r.t. x

$$14+9x^{2}-20x^{4}$$

Steps Using Derivative Rule for Sum

Combine 8x and 6x to get 14x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+14x-4x^{5}+2+3)$$

Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+14x-4x^{5}+5)$$

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}.

$$3\times 3x^{3-1}+14x^{1-1}+5\left(-4\right)x^{5-1}$$

Multiply 3 times 3.

$$9x^{3-1}+14x^{1-1}+5\left(-4\right)x^{5-1}$$

Subtract 1 from 3.

$$9x^{2}+14x^{1-1}+5\left(-4\right)x^{5-1}$$

Subtract 1 from 1.

$$9x^{2}+14x^{0}+5\left(-4\right)x^{5-1}$$

Multiply 1 times 14.

$$9x^{2}+14x^{0}-20x^{5-1}$$

Subtract 1 from 5.

$$9x^{2}+14x^{0}-20x^{4}$$

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

$$9x^{2}+14\times 1-20x^{4}$$

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

$$9x^{2}+14-20x^{4}$$