soit \( f \) la fonction définie sur \( ]-\infty ; 2[U] 2 ;+\infty[ \) par \( f(x)=\frac{x+1}{2-x} \). Démontrer que \( f \) est dérivable en 3 et donner la valeur de \( f^{\prime}(3) \).

\( d y ( d x - ( 1 - x ) y ^ { 2 } = ( 2 x - 1 ) y - x \)

Derivar las siguientes funciones 1. \( f(x)=(4 x+1)(6 x+3) \) 2. \( f(x)=(8-7 t)\left(t^{2}-2\right) \) 3. \( f(x)=\left(3 r^{2}-4\right)\left(r^{2}-5 r+1\right) \) 4. \( f(x)=\left(x^{2}+3 x-2\right)\left(2 x^{2}-x-3\right) \) 5. \( f(x)=\left(8 x^{2}+2 x-3\right)\left(5 x^{3}+2\right) \)

\( 1 \leftarrow \) The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( \mathrm{b}=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain mass (in grams). Suppose the brain mass of a 27 - g fetus is changing at a rate of 0.21 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \). \( \frac{\mathrm{dm}}{\mathrm{dt}}=\square \mathrm{g} \) per day (Round to five decimal places as needed.)

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and b is the brain ma: grams). Suppose the brain mass of a \( 21-\mathrm{g} \) fetus is changing at a rate of 0.26 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \). \( \frac{\mathrm{dm}}{\mathrm{dt}}=\square \mathrm{g} \) per day (Round to five decimal places as needed.)

The brain mass of a fetus can be estimated using the total mass of the fetus by the function \( b=0.22 \mathrm{~m}^{0.87} \), where m is the mass of the fetus (in grams) and \( b \) is the brain mass grams). Suppose the brain mass of a \( 20-\mathrm{g} \) fetus is changing at a rate of 0.23 g per day. Use this to estimate the rate of change of the total mass of the fetus, \( \frac{\mathrm{dm}}{\mathrm{dt}} \).