Obraich a-mach \(f\textquotesingle(x)\) nuair a tha \(f(x) = 12{x^{\frac{2}{3}}}\)
\[f\textquotesingle(x)=\frac{4}{3}{x^{-\frac{1}{3}}}\]
\[f\textquotesingle(x) = 8{x^{ - \frac{1}{3}}}\]
\[f\textquotesingle(x) = \frac{2}{3}{x^{ - \frac{1}{3}}}\]
Diofaraich \(y = \sqrt x (x + 1)\)
\[\frac{{dy}}{{dx}} = \frac{3}{2}{x^{\frac{1}{2}}} + \frac{1}{2}{x^{ - \frac{1}{2}}}\]
\[\frac{{dy}}{{dx}}={x^{\frac{3}{2}}} + {x^{\frac{1}{2}}}\]
\[\frac{{dy}}{{dx}} = \frac{1}{2}{x^{\frac{1}{2}}} - \frac{1}{2}{x^{ - \frac{1}{2}}}\]
Lorg an caisead aig an tansaint don lùb \(y = \frac{{x + 1}}{{\sqrt x }}\) aig a' phuing nuair a tha x = 4.
\[m = \frac{3}{{16}}\]
\[m = \frac{5}{2}\]
\[m = \frac{1}{2}\]
Obraich a-mach an reat atharrachaidh aig an fhuincsean \(h(x) = \frac{{(x + 1)(x - 1)}}{x}\) nuair a tha x = -1
\[h\textquotesingle(x)= - 2\]
\[h\textquotesingle(x) = \frac{1}{2}\]
\[h\textquotesingle(x)= 2\]
Diofaraich \(y = 4x - 2\sin x\)
\[\frac{{dy}}{{dx}} = 4 - 2\cos x\]
\[\frac{{dy}}{{dx}} = 4x - 2\cos x\]
\[\frac{{dy}}{{dx}} = 4 + 2\cos x\]
Diofaraich \(y = 5\cos x - 1\)
\[\frac{{dy}}{{dx}} = 5\sin x\]
\[\frac{{dy}}{{dx}} = - 5\sin x - x\]
\[\frac{{dy}}{{dx}} = - 5\sin x\]
Obraich a-mach \(\frac{{dy}}{{dx}}\) nuair a tha \(y = 7\sin x + \cos x\)
\[\frac{{dy}}{{dx}} = - 7\cos x - \sin x\]
\[\frac{{dy}}{{dx}} = 7\cos x + \sin x\]
\[\frac{{dy}}{{dx}} = 7\cos x - \sin x\]
Obraich a-mach \(\frac{{dy}}{{dx}}\) nuair a tha \(y = {({x^2} + 5)^{11}}\)
\[\frac{{dy}}{{dx}} = 11{({x^2} + 5)^{10}}\]
\[\frac{{dy}}{{dx}} = 22x{({x^2} + 5)^{10}}\]
\[\frac{{dy}}{{dx}} = 22{(2x)^{10}}\]
Diofaraich \(y = {(1 - x)^{ - \frac{1}{2}}}\)
\[\frac{{dy}}{{dx}} = \frac{1}{2}{(1 - x)^{ - \frac{3}{2}}}\]
\[\frac{{dy}}{{dx}} = - \frac{1}{2}{(1 - x)^{ - \frac{3}{2}}}\]
\[\frac{{dy}}{{dx}} = - \frac{1}{2}{(1 - x)^{ - \frac{1}{2}}}\]
Diofaraich \(y = \cos (1 + 2x)\)
\[\frac{{dy}}{{dx}} = 2\cos (1 + 2x)\]
\[\frac{{dy}}{{dx}} = - 2\sin (1 + 2x)\]
\[\frac{{dy}}{{dx}} = 2\sin (1 + 2x)\]
Diofaraich \(y = {(\cos 2x)^3}\)
\[\frac{{dy}}{{dx}} = - 6\sin 2x\,{\cos ^2}2x\]
\[\frac{{dy}}{{dx}} = - 2\sin 2x\,{\cos ^2}2x\]
\[\frac{{dy}}{{dx}} = - 3\sin 2x\,{\cos ^2}2x\]
Obraich a-mach co-aontar an tainsaint don lùb leis a' cho-aontar \(y = 3{x^2} + 2x - 5\) aig a' phuing far a bheil x = - 2
\[10x-y+17=0\]
\[8x-y+13=0\]
\[10x+y+17=0\]
Dè a' phuing no na puingean air lùb a' cho-aontair \(y = 5{x^3}\) aig a bheil an tansaint co-shìnte ris an loidhne leis a' cho-aontar \(15x - 4y + 8 = 0\)?
\(\left( {-\frac{1}{2},\frac{5}{8}} \right)\) agus \(\left( {\frac{1}{2},\frac{5}{8}} \right)\)
\[\left( {\frac{1}{2},\frac{5}{4}} \right)\]
\[\left( { - \frac{1}{4},\frac{5}{{16}}} \right)agus\left( {\frac{1}{4},\frac{5}{{16}}} \right)\]