SOLUTION: can someone help with these two questions thanks
1.)find y' when
y=7^2^x this problem is 7 with the 2x are small
2.) find y' when
y=x^5 5^x this problem is x to
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Question 201027: can someone help with these two questions thanks
1.)find y' when
y=7^2^x this problem is 7 with the 2x are small
2.) find y' when
y=x^5 5^x this problem is x to the power of 5 then 5 to the power of x
thanks so much
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
1) If )
then
}{dx} = b^u\ln(b)\frac{du}{dx})
So for 
, 
, so )
then:
}{dx} = \left(7^2^x\ln(7)\right)\left(2^x\ln(2)\right))
2) You have the product of two functions, so use the Product Rule:
If  = g(x) \cdot h(x))
then  = g(x)h'(x) + h(x)g'(x))
Here,  = x^5)
, so  = 5x^4)
(Power Rule)
and  = 5^x)
, so  = 5^x\ln(5))
(see Prob 1)
Putting it all together:
 = x^5\cdot 5^x)
 = x^5\cdot5^x\ln(5) + 5^x\cdot5x^4)
John
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