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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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$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(y^2\right)+\frac{d}{dx}\left(y\sin\left(x\right)\right)=x^3$
Learn how to solve problems step by step online. Find the implicit derivative d/dx(x+y^2ysin(x))=x^3. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function is equal to 1. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=y and g=\sin\left(x\right). The derivative of the linear function is equal to 1.