Final Answer
$12\sqrt{2}\sqrt{a^{7}}b^{3}+\frac{21\sqrt{2}}{2}b^{4}\sqrt{a^{5}}$
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Step-by-step Solution
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Simplifying
$\frac{d}{db}\left(b^{4}\sqrt{3a^2}\sqrt{6a^5}\right)$
Learn how to solve implicit differentiation problems step by step online.
$\frac{d}{db}\left(b^{4}\sqrt{3a^2}\sqrt{6a^5}\right)$
Learn how to solve implicit differentiation problems step by step online. Find the derivative of (3a^2)^1/2b^3(6a^5)^1/2b. Simplifying. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=b^{4} and g=\sqrt{3a^2}\sqrt{6a^5}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\sqrt{3a^2} and g=\sqrt{6a^5}. The power of a product is equal to the product of it's factors raised to the same power.
Final Answer
$12\sqrt{2}\sqrt{a^{7}}b^{3}+\frac{21\sqrt{2}}{2}b^{4}\sqrt{a^{5}}$