What is the d/(dL)(({K}(L)L)^{1/2}) ?

The d/(dL)(({K}(L)L)^{1/2}) is (L d/(dL)({K}(L))+{K}(L))/(2(L{K)(L))^{1/2}}

What is the first d/(dL)(({K}(L)L)^{1/2}) ?

The first d/(dL)(({K}(L)L)^{1/2}) is (L d/(dL)({K}(L))+{K}(L))/(2(L{K)(L))^{1/2}}

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\frac{d}{d L} ((K (L) L)^{\frac{1}{2}})

\frac{L \frac{d}{d L} ( K ( L ) ) + K ( L )}{2 ( L K ( L ) ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d L} ((K (L) L)^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( K ( L ) L ) ^{\frac{1}{2}}} \frac{d}{d L} (K (L) L)

= \frac{1}{2 ( K ( L ) L ) ^{\frac{1}{2}}} \frac{d}{d L} (K (L) L)

\frac{d}{d L} (K (L) L) = L \frac{d}{d L} (K (L)) + K (L)

= \frac{1}{2 ( K ( L ) L ) ^{\frac{1}{2}}} (L \frac{d}{d L} (K (L)) + K (L))

Simplify

\frac{1}{2 ( K ( L ) L ) ^{\frac{1}{2}}} (L \frac{d}{d L} (K (L)) + K (L)) : \frac{L \frac{d}{d L} ( K ( L ) ) + K ( L )}{2 ( L K ( L ) ) ^{\frac{1}{2}}}

= \frac{L \frac{d}{d L} ( K ( L ) ) + K ( L )}{2 ( L K ( L ) ) ^{\frac{1}{2}}}

\frac{s}{s + 5}

f (x) = 4 x^{3} - x^{2} - 7, at x = - 1

\int 8 tan (x) sec^{3} (x) d x

y = (x^{2} + 2)^{2} (x^{4} + 4)^{4}

\int \frac{1}{y ^{3} - y} d y

What is the d/(dL)(({K}(L)L)^{1/2}) ?
The d/(dL)(({K}(L)L)^{1/2}) is (L d/(dL)({K}(L))+{K}(L))/(2(L{K)(L))^{1/2}}
What is the first d/(dL)(({K}(L)L)^{1/2}) ?
The first d/(dL)(({K}(L)L)^{1/2}) is (L d/(dL)({K}(L))+{K}(L))/(2(L{K)(L))^{1/2}}