Solve {l}{(15x_{2})+(10x_{2})+(10x_{2})+(8x_{2})}{+(5*2)+(1*2)+(2*2)+(4*2)+(3*2)}

$$\left. \begin{array} { l } { ( 15 x _ { 2 } ) + ( 10 x _ { 2 } ) + ( 10 x _ { 2 } ) + ( 8 x _ { 2 } ) } \\ { + ( 5 \times 2 ) + ( 1 \times 2 ) + ( 2 \times 2 ) + ( 4 \times 2 ) + ( 3 \times 2 ) } \end{array} \right.$$

Evaluate

$$43x_{2}+30$$

Solution Steps

Multiply 5 and 2 to get 10. Multiply 1 and 2 to get 2. Multiply 2 and 2 to get 4. Multiply 4 and 2 to get 8. Multiply 3 and 2 to get 6.

$$15x_{2}+10x_{2}+10x_{2}+8x_{2}+10+2+4+8+6$$

Combine 15x_{2} and 10x_{2} to get 25x_{2}.

$$25x_{2}+10x_{2}+8x_{2}+10+2+4+8+6$$

Combine 25x_{2} and 10x_{2} to get 35x_{2}.

$$35x_{2}+8x_{2}+10+2+4+8+6$$

Combine 35x_{2} and 8x_{2} to get 43x_{2}.

$$43x_{2}+10+2+4+8+6$$

Add 10 and 2 to get 12.

$$43x_{2}+12+4+8+6$$

Add 12 and 4 to get 16.

$$43x_{2}+16+8+6$$

Add 16 and 8 to get 24.

$$43x_{2}+24+6$$

Add 24 and 6 to get 30.

$$43x_{2}+30$$

Differentiate w.r.t. x_2

$$43$$

Steps Using Derivative Rule for Sum

Multiply 5 and 2 to get 10. Multiply 1 and 2 to get 2. Multiply 2 and 2 to get 4. Multiply 4 and 2 to get 8. Multiply 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(15x_{2}+10x_{2}+10x_{2}+8x_{2}+10+2+4+8+6)$$

Combine 15x_{2} and 10x_{2} to get 25x_{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(25x_{2}+10x_{2}+8x_{2}+10+2+4+8+6)$$

Combine 25x_{2} and 10x_{2} to get 35x_{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(35x_{2}+8x_{2}+10+2+4+8+6)$$

Combine 35x_{2} and 8x_{2} to get 43x_{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(43x_{2}+10+2+4+8+6)$$

Add 10 and 2 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(43x_{2}+12+4+8+6)$$

Add 12 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(43x_{2}+16+8+6)$$

Add 16 and 8 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(43x_{2}+24+6)$$

Add 24 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x_{2}}(43x_{2}+30)$$

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}.

$$43x_{2}^{1-1}$$

Subtract 1 from 1.

$$43x_{2}^{0}$$

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

$$43\times 1$$

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

$$43$$