Find g'(x), if g(x) = 11x^{11} + 52x - 36.

Question:

Find {eq}g'(x), {/eq} if {eq}g(x) = 11x^{11} + 52x - 36. {/eq}

Power rule of differentiation:


To find the derivative of the given function we are going to use power rule of differentiation,

It states that the derivative of {eq}x^n {/eq} is {eq}nx^{n - 1} {/eq}, where {eq}n {/eq} is a real number.

Also, recall that the derivative of a constant function is zero.

Answer and Explanation:


Differentiating the function with respect to {eq}x {/eq},

$$\displaystyle \begin{align*} g'(x) &= \dfrac {d}{dx} \left [ 11x^{11} + 52x - 36 \right ] \\ &= \dfrac {d}{dx} \left [ 11x^{11} \right ] + \dfrac {d}{dx} \left [ 52x \right ] - \dfrac {d}{dx} \left [ 36 \right ] \\ &= 11\dfrac {d}{dx} \left [ x^{11} \right ] + 52\dfrac {d}{dx} \left [ x \right ] - 0 \\ &= 11 \left ( 11x^{10} \right ) + 52(1) \\ g'(x) &= 121x^{10} + 52 \\ \end{align*} $$


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