Question

Find the derivatives of the following using increment method.1.y = 6x² +10x - 3

Answer 1

Given

`y=6x²+10x-3`

Find

derivatives using increment method.

Step-by-step explanation

Given

`y=6x²+10x-3`

replace x and y by

`\begin{gathered} x+\Delta x \\ y+\Delta y \end{gathered}`

so ,

`\begin{gathered} y+\Delta y-y=6(x+\Delta x)^2+10(x+\Delta x)-3-(6x^2+10x-3) \\ \Delta y=6x^2+6\Delta^2x^2+12\Delta x^2+10x+10\Delta x-3-6x^2-10x+3 \\ \Delta y=12\Delta x^2+6\Delta^2x^2+10\Delta x \\ \end{gathered}`

now divide by

`\Delta x`

so ,

`\begin{gathered} y^(\prime)=(12\Delta x^2+10\Delta x+6\Delta^2x^2)/(\Delta x) \\ \\ y^(\prime)=12x+10+6\Delta x \end{gathered}`

now taking limit

`\begin{gathered} \lim_(\Delta x\to0)y^(\prime)=\lim_(\Delta x\to0)(12x+10+6\Delta x) \\ \\ y^(\prime)=12x+10 \end{gathered}`

Final Answer

Therefore , the derivative of the function using increment method is 12x + 10