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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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$\frac{d}{dx}\left(2x\left(1-2\sin\left(x\right)^2\right)\right)+\frac{d}{dx}\left(-4x^2\cos\left(x\right)\sin\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(2x(1-2sin(x)^2)-4x^2cos(x)sin(x)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the linear function is equal to 1.