What is the derivative of 0.5(x+a)^p-x ?

The derivative of 0.5(x+a)^p-x is 0.5p(x+a)^{p-1}-1

What is the first derivative of 0.5(x+a)^p-x ?

The first derivative of 0.5(x+a)^p-x is 0.5p(x+a)^{p-1}-1

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derivative of

0.5 (x + a)^{p} - x

0.5 p (x + a)^{p - 1} - 1

Solution steps

\frac{d}{d x} (0.5 (x + a)^{p} - x)

Treat

a, p

as constants

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (0.5 (x + a)^{p}) - \frac{d x}{d x}

\frac{d}{d x} (0.5 (x + a)^{p}) = 0.5 p (x + a)^{p - 1}

\frac{d x}{d x} = 1

= 0.5 p (x + a)^{p - 1} - 1

\int sin (3 x - 7) d x

\frac{d}{d t} (9 cos (t))

\int 8 sec^{4} (x) d x

\int 1 + sin (θ) d θ

f (x) = sin (x) - cos (x)

What is the derivative of 0.5(x+a)^p-x ?
The derivative of 0.5(x+a)^p-x is 0.5p(x+a)^{p-1}-1
What is the first derivative of 0.5(x+a)^p-x ?
The first derivative of 0.5(x+a)^p-x is 0.5p(x+a)^{p-1}-1