What is the derivative of f(x)=sqrt(x)-(x+6)^6 ?

The derivative of f(x)=sqrt(x)-(x+6)^6 is 1/(2sqrt(x))-6(x+6)^5

What is the first derivative of f(x)=sqrt(x)-(x+6)^6 ?

The first derivative of f(x)=sqrt(x)-(x+6)^6 is 1/(2sqrt(x))-6(x+6)^5

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derivative of

f (x) = x - (x + 6)^{6}

\frac{1}{2 x} - 6 (x + 6)^{5}

Solution steps

\frac{d}{d x} (x - (x + 6)^{6})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) - \frac{d}{d x} ((x + 6)^{6})

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} ((x + 6)^{6}) = 6 (x + 6)^{5}

= \frac{1}{2 x} - 6 (x + 6)^{5}

What is the derivative of f(x)=sqrt(x)-(x+6)^6 ?
The derivative of f(x)=sqrt(x)-(x+6)^6 is 1/(2sqrt(x))-6(x+6)^5
What is the first derivative of f(x)=sqrt(x)-(x+6)^6 ?
The first derivative of f(x)=sqrt(x)-(x+6)^6 is 1/(2sqrt(x))-6(x+6)^5