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Hi tutor,Using first principles, find the derivative of y=3x^2+5x-2 please? Here is an image of the formula if you need it:

Hi tutor,Using first principles, find the derivative of y=3x^2+5x-2 please? Here is-example-1
User Niko Craft
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1 Answer

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GIVEN

The function is given to be:


y=3x^2+5x-2

SOLUTION

The first principle formula is given to be:


f^(\prime)(x)=\lim_(h\to0)(f(x+h)-f(x))/(h)

Rewrite the function:


f(x)=3x^2+5x-2

Evaluate f(x + h):


\begin{gathered} f(x+h)=3(x+h)^2+5(x+h)-2 \\ Expand \\ f(x+h)=3x^2+6xh+3h^2+5x+5h-2 \end{gathered}

Substitute into the equation:


f^(\prime)(x)=\lim_(h\to0)(3x^2+6xh+3h^2+5x+5h-2-(3x^2+5x-2))/(h)

Simplify:


\begin{gathered} f^(\prime)(x)=\lim_(h\to0)(6xh+3h^2+5h)/(h) \\ \therefore \\ f^(\prime)(x)=\lim_(h\to0)(h(6x+3h+5))/(h) \\ f^(\prime)(x)=\lim_(h\to0)(6x+3h+5) \end{gathered}

Evaluate the limit:


f^(\prime)(x)=6x+5

Therefore, the derivative is:


f^(\prime)(x)=6x+5

User Kevin Old
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