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1. Differentiate each of the following: $(2,3,3,5,3,5,4,5,5$ marks $)$
a. $y=-3 x+5 e^{x}$

Answer

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Answer

$\boxed{dy/dx = 5e^x - 3}$

Steps

Step 1 ：Given the function: $y = -3x + 5e^x$

Step 2 ：We need to find the derivative of the function with respect to x.

Step 3 ：Using the power rule for differentiation, the derivative of $-3x$ is $-3$.

Step 4 ：Using the chain rule for differentiation, the derivative of $5e^x$ is $5e^x$.

Step 5 ：Combining the derivatives, we get: $dy/dx = -3 + 5e^x$

Step 6 ：$\boxed{dy/dx = 5e^x - 3}$