Welcome to Workshop One! Below are the questions with working. I'd recommend you either open the Identity Sheet in a new tab, display it on a separate monitor or have it printed beside you!
Question 1: Hyperbolic Expressions. Write the following as algebraic expressions of x.
a) \( \sinh(log_e x) \)
We know from our Identity Sheet that \( \sinh(x) = \frac {1}{2} (e^x - e^{-x}) \)
Substituting in \( log_e x \) gives us \( \sinh(x) = \frac {1}{2} (e^{\ln(x)} - e^{-ln(x)}) \)
We know from our Logarithmic Laws that \( e^{ln(x)} = x \)
\( \frac {dy}{dx} = \frac {2y- 2yx log_e y}{2x^2 y + x \sqrt y} \)
c) \( 4\cos(x)\sin(y) = 1 \)
We know from our Identity Sheet that \( \frac{d}{dx} = \frac {dy}{dx} * \frac {d}{dy} \) the product rule is uv = u'v + uv' applying this to the question yields: