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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
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$\frac{d}{db}\left(b\right)\sqrt[3]{54ax^{14}}x^{12}+b\left(\frac{d}{db}\left(\sqrt[3]{54ax^{14}}\right)x^{12}+\sqrt[3]{54ax^{14}}\frac{d}{db}\left(x^{12}\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of b(54ax^14)^1/3x^12. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power of a product is equal to the product of it's factors raised to the same power. The derivative of the linear function is equal to 1. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.