pochodne

[aniluap1081]

obliczyć pochodne
a) y = 3tg^2 ( 2x^3 + 5)
b)y= (4x^2 + 5x) / sin x
c)y= (arctgx) / (3x^2 +5)
d) y= x^3 * e^sin2x

[Lbubsazob]

a)
\(y=3 \left(\tan(2x^3+5) \right)^2 \\
y'=6\tan(2x^3+5) \cdot \frac{1}{\cos^2 \left(2x^3+5 \right) } \cdot 6x^2\)

b)
\(y= \frac{4x^2+5x}{\sin x} \\
y'= \frac{(8x+5)\sin x-\cos x(4x^2+5x)}{\sin^2 x}\)

[Lbubsazob]

c)
\(y= \frac{\arctan x}{3x^2+5} \\
y'= \frac{ \frac{1}{1+x^2} \cdot (3x^2+5)-6x\arctan x }{(3x^2+5)^2}\)

d)
\(y=x^3 e^{\sin 2x} \\
y'=3x^2e^{\sin 2x}+x^3 e^{\sin 2x} \cdot 2\cos 2x\)