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amania_r
Lv 7
amania_r asked in Science & MathematicsMathematics · 2 years ago

Differentiation question?

Hi. Any tips on how to differentiate:

y = a + bx + sqrt( c + dx^2)

with respect to x. I don't think I can use the chain rule because x is in two different places.

Thanks

3 Answers

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  • Φ² = Φ+1
    Lv 7
    2 years ago
    Favorite Answer

    dy/dx = da/dx + d(bx)/dx + d(sqrt( c + dx^2))/dx

    dy/dx = 0 + b + dx / sqrt(c + dx^2)

    dy/dx = dx / sqrt(c + dx^2) + b

  • Como
    Lv 7
    2 years ago

    dy/dx = b + (1/2) ( c + dx² ) ^(-1/2) (2dx )

    dy/dx = b + dx / ( c + dx² )

  • billrussell42
    Lv 7
    2 years ago

    you use (f + g)' = f' + g'

    and the chain rule on the right hand part

    y = a + bx + √( c + dx²)

    y' = b + (√( c + dx²) )'

    y' = b + (( c + dx²)^-1/2)(2dx)

    y' = b + 2dx/√( c + dx²)

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