DẠNG 1. KHÁI NIỆM ĐẠO HÀM, ĐẠO HÀM CỦA MỘT SỐ HÀM SỐ THƯỜNG GẶP, CÔNG THỨC ĐẠO HÀM

-4.

4.

\(\frac{1}{4}.\)

\( - \frac{1}{4}.\)

\({u^\prime }(x) - {v^\prime }(x).\)

\({{\rm{u}}^\prime }({\rm{x}}) \cdot {{\rm{v}}^\prime }({\rm{x}}).\)

\({u^\prime }(x) + {v^\prime }(x).\)

\(\frac{{{u^\prime }(x)}}{{{v^\prime }(x)}}.\)

\({u^\prime }(x)v(x) + u(x){v^\prime }(x).\)

\({u^\prime }(x)v(x) - u(x){v^\prime }(x).\)

\({u^\prime }(x)v(x) + u(x)v(x).\)

\(u(x)v(x) + u(x){v^\prime }(x).\)

\(\frac{{u(x) \cdot {v^\prime }(x) - {u^\prime }(x) \cdot v(x)}}{{{v^2}(x)}}.\)

\(\frac{{{u^\prime }(x) \cdot v(x) - u(x) \cdot {v^\prime }(x)}}{{v(x)}}.\)

\(\frac{{u(x) \cdot {v^\prime }(x) - {u^\prime }(x) \cdot v(x)}}{{v(x)}}.\)

\(\frac{{{u^\prime }(x) \cdot v(x) - u(x) \cdot {v^\prime }(x)}}{{{v^2}(x)}}.\)

\(\frac{{ - {{\rm{v}}^\prime }({\rm{x}})}}{{{{\rm{v}}^2}({\rm{x}})}}.\)

\(\frac{{{v^\prime }(x)}}{{{v^2}(x)}}.\)

\(\frac{{ - {{\rm{v}}^\prime }({\rm{x}})}}{{{\rm{v}}({\rm{x}})}}.\)

\(\frac{{{{\rm{v}}^\prime }({\rm{x}})}}{{{\rm{v}}({\rm{x}})}}.\)

\(\frac{{{{\rm{u}}^\prime }({\rm{x}})}}{{2\sqrt {{\rm{u}}({\rm{x}})} }}.\)

\(\frac{1}{{2\sqrt {{\rm{u}}({\rm{x}})} }}.\)

\(\frac{{{{\rm{u}}^\prime }({\rm{x}})}}{{\sqrt {{\rm{u}}({\rm{x}})} }}.\)

\(\frac{{u(x)}}{{2\sqrt {{u^\prime }(x)} }}.\)

\({\left( {{\pi ^9}} \right)^\prime } = 9{\pi ^8}.\)

\({\left( {{\pi ^9}} \right)^\prime } = {\pi ^8}.\)

\({\left( {{\pi ^9}} \right)^\prime } = \frac{{{\pi ^{10}}}}{{10}}.\)

\({\left( {{\pi ^9}} \right)^\prime } = 0.\)

\({(x)^\prime } = \frac{{{x^2}}}{2}.\)

\({({\rm{x}})^\prime } = 1.\)

\({({\rm{x}})^\prime } = 0.\)

\({(x)^\prime } = {x^2}.\)

\({{\rm{x}}^{{\rm{n}} - 1}}.\)

\({\rm{n}}{{\rm{x}}^{\rm{n}}}.\)

\({\rm{n}}{{\rm{x}}^{{\rm{n}} - 1}}.\)

\(\frac{{{{\rm{x}}^{{\rm{n}} + 1}}}}{{{\rm{n}} + 1}}.\)

\(\frac{1}{{2\sqrt {\rm{x}} }}.\)

\(\frac{1}{{\sqrt {\rm{x}} }}.\)

\(\frac{2}{3}\sqrt {{{\rm{x}}^3}} .\)

\(\sqrt {{{\rm{x}}^3}} .\)

\(\sin x.\)

\(\cos x.\)

\( - \sin {\rm{x}}.\)

\( - \cos x.\)

\(\sin x.\)

\(\cos x.\)

\( - \sin {\rm{x}}.\)

\( - \cos x.\)

\(\frac{1}{{{{\sin }^2}x}}.\)

\(\frac{{ - 1}}{{{{\sin }^2}x}}.\)

\(\frac{{ - 1}}{{{{\cos }^2}x}}.\)

\(\frac{1}{{{{\cos }^2}x}}.\)

\(\frac{1}{{{{\sin }^2}x}}.\)

\(\frac{{ - 1}}{{{{\sin }^2}x}}.\)

\(\frac{{ - 1}}{{{{\cos }^2}{\rm{x}}}}.\)

\(\frac{1}{{{{\cos }^2}x}}.\)

\(\cos ({\rm{ax}} + {\rm{b}}).\)

\( - \cos ({\rm{ax}} + {\rm{b}}).\)

\( - {\rm{acos}}({\rm{ax}} + {\rm{b}}).\)

\({\rm{a}}\cos ({\rm{ax}} + {\rm{b}}).\)

\( - \sin (ax + b).\)

\(\sin ({\rm{ax}} + {\rm{b}}).\)

\( - {\rm{a}}\sin ({\rm{ax}} + {\rm{b}}).\)

\({\rm{a}}\sin ({\rm{ax}} + {\rm{b}}).\)

\(\frac{{\rm{a}}}{{\sqrt {{\rm{ax}} + {\rm{b}}} }}.\)

\(\frac{{\rm{a}}}{{2\sqrt {{\rm{ax}} + {\rm{b}}} }}.\)

\(\frac{1}{{2\sqrt {{\rm{ax}} + {\rm{b}}} }}.\)

\(\frac{1}{{\sqrt {{\rm{ax}} + {\rm{b}}} }}.\)

\(\frac{{{\rm{ad}} + {\rm{bc}}}}{{{{({\rm{cx}} + {\rm{d}})}^2}}}.\)

\(\frac{{ - {\rm{ad}} + {\rm{bc}}}}{{{{({\rm{cx}} + {\rm{d}})}^2}}}.\)

\(\frac{{{\rm{ad}} - {\rm{bc}}}}{{{\rm{cx}} + {\rm{d}}}}.\)

\(\frac{{{\rm{ad}} - {\rm{bc}}}}{{{{({\rm{cx}} + {\rm{d}})}^2}}}.\)

-9.

-18.

-8.

0.

-2.

-1.

0.

2.