What is the derivative of x^8+x^{1/8} ?

The derivative of x^8+x^{1/8} is (1+64x^{63/8})/(8x^{7/8)}

What is the first derivative of x^8+x^{1/8} ?

The first derivative of x^8+x^{1/8} is (1+64x^{63/8})/(8x^{7/8)}

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derivative of

x^{8} + x^{\frac{1}{8}}

\frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}

Solution steps

\frac{d}{d x} (x^{8} + x^{\frac{1}{8}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (x^{8}) + \frac{d}{d x} (x^{\frac{1}{8}})

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} (x^{\frac{1}{8}}) = \frac{1}{8 x ^{\frac{7}{8}}}

= 8 x^{7} + \frac{1}{8 x ^{\frac{7}{8}}}

Simplify

8 x^{7} + \frac{1}{8 x ^{\frac{7}{8}}} : \frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}

= \frac{1 + 64 x ^{\frac{63}{8}}}{8 x ^{\frac{7}{8}}}

2 cos (2 + x^{3})

lo g_{10} (x^{2} + x + 1)

f (x) = \frac{3 ^{x}}{x}

f (x) = \frac{4}{t} - \frac{1}{6} t^{3} + \frac{8}{t ^{5}}

3 x^{2} (1 - x)^{3}

What is the derivative of x^8+x^{1/8} ?
The derivative of x^8+x^{1/8} is (1+64x^{63/8})/(8x^{7/8)}
What is the first derivative of x^8+x^{1/8} ?
The first derivative of x^8+x^{1/8} is (1+64x^{63/8})/(8x^{7/8)}