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C4 Differentiation Question

Given that y=2^x and using the result 2^x = e^(xln2), or otherwise,

show that dy/dx = 2^x ln2

Then find the gradient of the curve with equation y = 2^(x^2) at point (2,16)

Cheers
Reply 1
Avatar for .raiden.
.raiden.
10
Have you tried differentiating y=e^(xln2) ?

What have you done so far?
Reply 2
Avatar for .raiden.
.raiden.
10
ddxe2x=2e2x\frac{d}{dx} e^{2x} = 2e^{2x}

Does this help?
Reply 3
Avatar for paper-may
paper-may
7
y=2^x
=e^(xln(2))
=e^(ln(2^x))

Use y=e^xln(2)

So,

dy/dx=ln(2)*e^(xln(2))
=ln(2)*e^ln(2^x)
=ln(2)*(2^x)
=(2^x)*ln(2)
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by paper-may

...


Are you aware of the forum guidelines that ask us not to post full solutions
Reply 5
Avatar for paper-may
paper-may
7
Original post by TenOfThem
Are you aware of the forum guidelines that ask us not to post full solutions


Clearly not.
Reply 6
Avatar for TenOfThem
TenOfThem
18
Original post by paper-may
Clearly not.


Front page of maths
Just above the non-sticky threads

http://www.thestudentroom.co.uk/showthread.php?t=403989

Asks us all to read before posting
Reply 7
Avatar for paper-may
paper-may
7
Original post by TenOfThem
Front page of maths
Just above the non-sticky threads

http://www.thestudentroom.co.uk/showthread.php?t=403989

Asks us all to read before posting


Ain't nobody got time for that.
Reply 8
Avatar for TenOfThem
TenOfThem
18
Original post by paper-may
Ain't nobody got time for that.


whatever

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