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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{db}\left(a^2b^8\right)+\frac{d}{db}\left(-c^2\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of a^2b^8-c^2. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (-c^2) is equal to zero. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.