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What is the derivative of y equals the quantity 2x plus 5 raised to 8 plus 4x all raised to3?
Wiki User
∙ 13y ago
I am interpreting this as:
Find the derivative of:
y=((2x+5)8+4x)3
To find the derivative (y'), the chain rule must be applied. The "outermost" function of this compound function is t3 (t being an arbitrary quantity). The derivative of t3 is 3t2 * dt, where "dt" is the derivative of the quantity "t". Applying this, we arrive at a working definition of y':
y' = 3((2x+5)8+4x)2(derivative of (2x+5)8+4x)
The derivative of (2x+5)8+4x is found using basic derivative definitions and the chain rule again:
8(2x+5)7(2)+4 = 16(2x+5)7+4
So now we can write y' again:
y'= 3((2x+5)8+4x)2(16(2x+5)7+4) = 48((2x+5)8+4x)2((2x+5)7+4)
This can be further simplified, but this is an arduous process. If you need further simplification, feel free to contact me via private message.
Wiki User
∙ 13y ago
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