Let \( y=\sin x \cdot \cos x \), then \( d y= \)

Use the fact that the derivative of the function \( g(x)=\sqrt{x} \) is \( g^{\prime}(x)=\frac{1}{2 \sqrt{x}} \) to find the equation of the tangent line to the graph of \( g(x) \) at the point \( x=81 \).

Choose the correct answer from those givens: (1) If \( \operatorname{Lim}_{x \rightarrow 0} \frac{\cos x-\cos ^{a} x}{x^{2}}=1 \), then \( a=\ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) } 1 & \text { (b) zero } & \text { (c) } 2 & \text { (d) } 3\end{array} \)

Determine the first derivative of the \( 1.1 \quad y=x^{3}-\cot \left(x^{3}+3 x-1\right) \)

Application 3: Simplifier les expressions suivantes: \( \begin{array}{ll}A=\ln (\sqrt{3})+\ln 3-\ln 9 & ; \\ C=\ln \left(\frac{1}{3}\right)+\ln \left(\frac{3}{5}\right)+\ln \left(\frac{5}{7}\right)+\ln \left(\frac{7}{9}\right) & ;\end{array} \quad D=\ln (\sqrt[3]{2}-\ln 16 \)

(iv) In integral equation of the form \( \int_{0}^{1} \frac{F(u) d u}{(t-u)^{n}}=G(t) \) is called. (a) Exact equation (b) Convolution type (c) Integro-differential equation (d) Abel's equation