Question 2: Find the derivative of y with respect to t.

$$ y=4\sqrt{t}\tanh\sqrt{t} $$

• Solution:

Question 3: Find the derivative of y with respect to v.

$$ y=\ln(\cosh(5v))-\frac{1}{2}\tanh^2(5v) $$

• Solution:

Question 5: Find the derivative of y with respect to $\theta$.

$$ y=\sinh(3\theta)(1-\ln(\sinh(3\theta))) $$

• Solution:

Question 6: Find the derivative of y with respect to x.

(Hint: before differentiating, express in terms of exponentials and simplify)

$$ y=(x^2+1)\,\text{sech}(\ln x) $$

• Solution:

Question 7: Find the derivative of y with respect to x for

$$ y=\sinh^{-1}(11\sqrt{15x}) $$

• Solution: