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Implicit Differentiation
Not all equations can be written like y = f(x), so taking the derivative can be tricky. Save the mess and do it directly with implicit differentiation.
Consider the function
\( f(x) = \sqrt{x+\sqrt{x+\sqrt{x+\ldots}}} \)
If the gradient of the tangent of the function at \( x = 12 \) can be expressed as \( \frac{a}{b} \) where \( a \) and \( b \) are positive coprime integers, what is the value of \( a + b \).
by
Cole Coupland
\[ \sin ( x + y ) = \log ( x + y ) \]
Find the value of \( \frac {dy}{dx}\).
Note that we didn't give you the base of the logarithm, you should not specifically assume that the logarithm is in base \(e\) or 10.
by
Vaibhav Prasad
If \({ x }^{ y }={ e }^{ x-y }\), then \(\frac { dy }{ dx } =\)
by
Dinesh Nath Goswami
by
Rohit Ner
Consider the function \( f(x) = \dfrac{x}{1+\dfrac{x}{1+\dfrac{x}{1+\ddots}}} \). Determine the value of \( f'(0) \).
by
Cole Coupland