7. (8 points) Circle True or False:
(a) $(\mathrm{T} / \mathrm{F})$ If $f$ is continuous at $a$, then $f$ is differentiable at $a$.
(b) (T/F) If $f$ and $g$ are differentiable, then $\frac{d}{d x}[f(x) g(x)]=f^{\prime}(x) g^{\prime}(x)$
(c) $(\mathrm{T} / \mathrm{F}) \frac{d}{d x}\left(\tan ^{2} x\right)=\frac{d}{d x}\left(\sec ^{2} x\right)$
(d) (T/F) Circle True.

Step 1 ：The problem is about the properties of continuous and differentiable functions.

Step 2 ：For part (a), the statement is false. A function can be continuous at a point but not differentiable. For example, the absolute value function is continuous everywhere but not differentiable at x=0.

Step 3 ：For part (b), the statement is false. According to the product rule of differentiation, the derivative of the product of two functions is not the product of their derivatives. Instead, it is given by \(f'(x)g(x) + f(x)g'(x)\).

Step 4 ：For part (c), the statement is false. The derivative of \(\tan^2x\) is \(2\tan(x)\sec^2(x)\), while the derivative of \(\sec^2x\) is \(2\sec(x)\sec(x)\tan(x)\). These are not equal.

Step 5 ：For part (d), the statement is not clear. It just says 'Circle True.' Without a specific statement to evaluate, we cannot determine if it is true or false.

Step 6 ：Final Answer: \(\boxed{\text{(a) False, (b) False, (c) False, (d) Cannot be determined}}\)