Solve 5x^3+x+58div2x^2+10x+8=

$$5 x ^ { 3 } + x + 58 \div 2 x ^ { 2 } + 10 x + 8 =$$

Evaluate

$$5x^{3}+29x^{2}+11x+8$$

Solution Steps

Divide 58 by 2 to get 29.

$$5x^{3}+x+29x^{2}+10x+8$$

Combine x and 10x to get 11x.

$$5x^{3}+11x+29x^{2}+8$$

Differentiate w.r.t. x

$$\left(3x+11\right)\left(5x+1\right)$$

Steps Using Derivative Rule for Sum

Divide 58 by 2 to get 29.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+x+29x^{2}+10x+8)$$

Combine x and 10x to get 11x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+11x+29x^{2}+8)$$

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}.

$$3\times 5x^{3-1}+11x^{1-1}+2\times 29x^{2-1}$$

Multiply 3 times 5.

$$15x^{3-1}+11x^{1-1}+2\times 29x^{2-1}$$

Subtract 1 from 3.

$$15x^{2}+11x^{1-1}+2\times 29x^{2-1}$$

Subtract 1 from 1.

$$15x^{2}+11x^{0}+2\times 29x^{2-1}$$

Multiply 1 times 11.

$$15x^{2}+11x^{0}+58x^{2-1}$$

Subtract 1 from 2.

$$15x^{2}+11x^{0}+58x^{1}$$

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

$$15x^{2}+11x^{0}+58x$$

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

$$15x^{2}+11\times 1+58x$$

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

$$15x^{2}+11+58x$$