The calculator will find the derivative of
1−x2, with steps shown.
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Implicit Differentiation Calculator with Steps
Solution
The function 1−x2 is the composition f(g(x)) of two functions f(u)=u and g(x)=1−x2.
Apply the chain rule dxd(f(g(x)))=dud(f(u))dxd(g(x)):
(dxd(1−x2))=(dud(u)dxd(1−x2))Apply the power rule dud(un)=nun−1 with n=21:
(dud(u))dxd(1−x2)=(2u1)dxd(1−x2)Return to the old variable:
2(u)dxd(1−x2)=2(1−x2)dxd(1−x2)The derivative of a sum/difference is the sum/difference of derivatives:
21−x2(dxd(1−x2))=21−x2(dxd(1)−dxd(x2))The derivative of a constant is 0:
21−x2(dxd(1))−dxd(x2)=21−x2(0)−dxd(x2)Apply the power rule dxd(xn)=nxn−1 with n=2:
−21−x2(dxd(x2))=−21−x2(2x)Thus, dxd(1−x2)=−1−x2x.
Answer
dxd(1−x2)=−1−x2xA