1-22 Differentiate the function.
To find: The derivative of the function y=x+xx2.
The derivative of the function y=x+xx2 is −32x−52−x−2_.
The function, y=x+xx2.
The Power Rule:
If n is any real number, then the power rule is,
The Sum Rule:
If f(x) and g(x) are both differentiable functions, then the sum rule is,
The derivative of y is dydx, which is obtained as follows:
dydx=ddx((x12×x−2)+(x×x−2))= ddx((x12−2)+(x1−2)) = ddx((x12−42)+(x1−2)) = ddx((x−32)+(x−1))
Apply the sum rule as shown in equation (2).
Apply the power rule as shown in equation (1).
Therefore, the derivative of the function y=x+xx2 is −32x−52−x−2_.