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Harley Ewing
Mathematics
22 July, 21:36
Find the dervite of y=X^2 + x + 1
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Regan Rosales
22 July, 21:51
0
y' (x) = 1 + 2 x
Step-by-step explanation:
Find the derivative of the following via implicit differentiation:
d/dx (y) = d/dx (1 + x + x^2)
Using the chain rule, d/dx (y) = (dy (u)) / (du) (du) / (dx), where u = x and d / (du) (y (u)) = y' (u):
d/dx (x) y' (x) = d/dx (1 + x + x^2)
The derivative of x is 1:
1 y' (x) = d/dx (1 + x + x^2)
Differentiate the sum term by term:
y' (x) = d/dx (1) + d/dx (x) + d/dx (x^2)
The derivative of 1 is zero:
y' (x) = d/dx (x) + d/dx (x^2) + 0
Simplify the expression:
y' (x) = d/dx (x) + d/dx (x^2)
The derivative of x is 1:
y' (x) = d/dx (x^2) + 1
Use the power rule, d/dx (x^n) = n x^ (n - 1), where n = 2.
d/dx (x^2) = 2 x:
Answer: y' (x) = 1 + 2 x
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Matilda Vaughn
22 July, 21:55
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2x + 1.
Step-by-step explanation:
y=x^2 + x + 1
Using the algebraic derivative rule, if y = ax^n then y' = anx^ (n-1):
The derivative is 2x^ (2 - 1) + 1x^ (1-1)
= 2x^1 + x^0
= 2x + 1.
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