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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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$\frac{d}{dz}\left(\sin\left(xyz^2\right)^3\right)+\frac{d}{dz}\left(-2\right)+\frac{d}{dz}\left(5ye^{y^2z}\right)$
Learn how to solve problems step by step online. Find the derivative d/dz(sin(xyz^2)^3-25ye^(y^2z)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=y and g=5e^{y^2z}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=e^{y^2z} and g=5. The derivative of the constant function (-2) is equal to zero.