What is (\partial)/(\partial L)(bL^3{K}(b)(b)^2) ?

The answer to (\partial)/(\partial L)(bL^3{K}(b)(b)^2) is 3L^2b^3{K}(b)

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(\partial)/(\partial L)(bL^3{K}(b)(b)^2)

\frac{\partial}{\partial L} (b L^{3} K (b) (b)^{2})

3 L^{2} b^{3} K (b)

Solution steps

\frac{\partial}{\partial L} (b L^{3} K (b) (b)^{2})

Simplify

b L^{3} K (b) (b)^{2} : L^{3} b^{3} K (b)

= \frac{\partial}{\partial L} (L^{3} b^{3} K (b))

Treat

b

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= b^{3} K (b) \frac{\partial}{\partial L} (L^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= b^{3} K (b) \cdot 3 L^{3 - 1}

Simplify

= 3 L^{2} b^{3} K (b)

y = \frac{( x ^{2} - 1 )}{( x ^{2} + x + 1 )}

\frac{d}{d x} (6 x^{\frac{3}{2}} sec (x))

x^{2} y^{^{''}} - x y^{^{'}} + y = 0, y = x

\frac{d}{d x} (- 0.4 x^{2} + 2.2 x + 4.7)

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

What is (\partial)/(\partial L)(bL^3{K}(b)(b)^2) ?
The answer to (\partial)/(\partial L)(bL^3{K}(b)(b)^2) is 3L^2b^3{K}(b)