Final Answer
$\frac{30k^7}{\sqrt[10]{l^{7}}}$
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Step-by-step Solution
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1
Simplify the derivative by applying the properties of logarithms
$\frac{d}{dl}\left(100\sqrt[10]{l^{3}}k^7\right)$
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$\frac{d}{dl}\left(100\sqrt[10]{l^{3}}k^7\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 100l^3^1/10k^7. Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant (100) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (k^7) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.
Final Answer
$\frac{30k^7}{\sqrt[10]{l^{7}}}$