What is the d/(dL)((2L+{K}(L))^{1/3}) ?

The d/(dL)((2L+{K}(L))^{1/3}) is (2+d/(dL)({K}(L)))/(3(2L+{K)(L))^{2/3}}

What is the first d/(dL)((2L+{K}(L))^{1/3}) ?

The first d/(dL)((2L+{K}(L))^{1/3}) is (2+d/(dL)({K}(L)))/(3(2L+{K)(L))^{2/3}}

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\frac{d}{d L} ((2 L + K (L))^{\frac{1}{3}})

\frac{2 + \frac{d}{d L} ( K ( L ) )}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}}

Solution steps

\frac{d}{d L} ((2 L + K (L))^{\frac{1}{3}})

Apply the chain rule:

\frac{1}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}} \frac{d}{d L} (2 L + K (L))

= \frac{1}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}} \frac{d}{d L} (2 L + K (L))

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

= \frac{1}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}} (2 + \frac{d}{d L} (K (L)))

Simplify

\frac{1}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}} (2 + \frac{d}{d L} (K (L))) : \frac{2 + \frac{d}{d L} ( K ( L ) )}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}}

= \frac{2 + \frac{d}{d L} ( K ( L ) )}{3 ( 2 L + K ( L ) ) ^{\frac{2}{3}}}

x \to 0 lim (x^{2} cos^{2} (2 x))

\int_{0}^{2 π} - sin^{2} (x) d x

s \to 0 lim (\frac{4}{1 + 2 ^{\frac{1}{s}}})

\frac{d}{d x} (\frac{x + 1}{x ^{2} + 1})

\frac{d}{d x} (2 x e^{- 2 x} - 2 x^{2} e^{- 2 x})

What is the d/(dL)((2L+{K}(L))^{1/3}) ?
The d/(dL)((2L+{K}(L))^{1/3}) is (2+d/(dL)({K}(L)))/(3(2L+{K)(L))^{2/3}}
What is the first d/(dL)((2L+{K}(L))^{1/3}) ?
The first d/(dL)((2L+{K}(L))^{1/3}) is (2+d/(dL)({K}(L)))/(3(2L+{K)(L))^{2/3}}