Final answer to the problem
$e^{\left(4x+\sin\left(x\right)-10\right)}+xe^{\left(4x+\sin\left(x\right)-10\right)}\left(4+\cos\left(x\right)\right)$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative of xe^(4x+sin(x)+-10). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=e^{\left(4x+\sin\left(x\right)-10\right)}. The derivative of the linear function is equal to 1. Applying the derivative of the exponential function. The derivative of a sum of two or more functions is the sum of the derivatives of each function.
Final answer to the problem
$e^{\left(4x+\sin\left(x\right)-10\right)}+xe^{\left(4x+\sin\left(x\right)-10\right)}\left(4+\cos\left(x\right)\right)$
