Question

Evaluate the following. d/dx(10^x + e^2)

Answer 1

d/dx[10x+e2]
=d/dx[10x]+d/dx[e2}
=ln(10)⋅10x+0
=ln(10)⋅10x

Answer 2

$\large\begin{array}{l} \textsf{Finding the derivative of}\\\\ \mathsf{f(x)=10^x+e^2}\\\\\\ \textsf{You can differentiate it using basic rules:}\\\\ \mathsf{\dfrac{df}{dx}=\dfrac{d}{dx}\!\left(10^x+e^2\right)}\\\\ \mathsf{\dfrac{df}{dx}=\dfrac{d}{dx}(10^x)+\dfrac{d}{dx}(e^2)}\\\\ \mathsf{\dfrac{df}{dx}=10^x\cdot \ell n\,10+0\qquad\quad\textsf{(since }e^2\textsf{ is a constant)}}\\\\\\ \therefore~~\boxed{\begin{array}{l} \begin{array}{c}\mathsf{\dfrac{df}{dx}=10^x\,\ell n\,10} \end{array} \end{array}}\qquad\checkmark \end{array}$


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Tags: derivative function evaluate sum exponential constant basic rule differentiation differential calculus