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Second derivative of y = \ln(x)?

Implicit derivative of x^2 + y^2 = 25?

Ch12 collection

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Put your calculus skills to the test with questions on derivatives and implicit differentiation

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Answers

1
Implicit derivative of x^2 + y^2 = 25?
dy/dx = 2x + 2y
dy/dx = -x/y
dy/dx = y/x
dy/dx = x/y
2
Second derivative of y = \ln(x)?
\ln(x)
-1/x^2
1/x
x
3
Derivative of f(x) = x^{2x}?
x^{2x}(2 + 2\ln(x))
2x^{2x-1}
2x\ln(x)
x^{2x}\ln(x^2)
4
Derivative of \ln(x^2 + 1)?
1/(x^2 + 1)
2x\ln(x^2 + 1)
\ln(2x)
2x/(x^2 + 1)
5
Derivative of e^{3x}?
e^{3x}
\ln(3x)
3e^{3x}
3x\c\dot e^{3x}
6
Derivative of y = \frac{x}{\ln(x)}?
[\ln(x) - 1]/[\ln(x)]^2
\ln(x)/x
x\c\dot \ln(x)
1/\ln(x)