differential of y=10√x-e^2x Watch

ltorrington
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#1
Report Thread starter 9 years ago
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what is the differential of y=10√x-e^2x

is it y'=5x^-0.5-e^(2x)?
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steve2005
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(Original post by ltorrington)
what is the differential of y=10√x-e^2x

is it y'=5x^-0.5-e^(2x)?
No


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jj193
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y'=5x^-0.5-e^(2x)?
almost, wrong for the -e^2x
you do this:
d(-e^2x)/dx = -e^2x * (d(2x)/dx)
" " = -2e^2x

It's by chain rule, differentiate the whole thing, and then differentiate the exponent (Power), and multiply the whole things by that.
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ltorrington
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thanks =] , just couldn't remember about what to do with the e
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Totally Tom
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(Original post by ltorrington)
what is the differential of y=10√x-e^2x

is it y'=5x^-0.5-e^(2x)?
do you mean y=10\sqrt{x-e^{2x}} or y=10\sqrt{x}-e^{2x}?
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Unbounded
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(Original post by ltorrington)
thanks =] , just couldn't remember about what to do with the e
More generally, again due to chain rule, we find that  y = e^{f(x)} \implies \dfrac{\mathrm{d}y}{\mathrm{d}x} = f'(x) \times e^{f(x)} where f(x) is some function of x.

For example,  y = e^{x^3+2} \implies \dfrac{\mathrm{d}y}{\mathrm{d}x} = 3x^2 \times e^{x^3+2}

And also,  y = e^{\sin x} \implies \dfrac{\mathrm{d}y}{\mathrm{d}x} = \cos x \times e^{\sin x}
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