What is the derivative of (4/5 x^5) ?

The derivative of (4/5 x^5) is (1024x^4)/(625)

What is the first derivative of (4/5 x^5) ?

The first derivative of (4/5 x^5) is (1024x^4)/(625)

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\frac{d}{d x} ((\frac{4}{5} x)^{5})

\frac{1024 x ^{4}}{625}

Solution steps

\frac{d}{d x} ((\frac{4}{5} x)^{5})

Apply the chain rule:

5 (\frac{4}{5} x)^{4} \frac{d}{d x} (\frac{4}{5} x)

= 5 (\frac{4}{5} x)^{4} \frac{d}{d x} (\frac{4}{5} x)

\frac{d}{d x} (\frac{4}{5} x) = \frac{4}{5}

= 5 (\frac{4}{5} x)^{4} \frac{4}{5}

Simplify

5 (\frac{4}{5} x)^{4} \frac{4}{5} : \frac{1024 x ^{4}}{625}

= \frac{1024 x ^{4}}{625}

\int \frac{x}{( x ^{4} + 2 )} d x

t y^{^{'}} + 2 y = sin (t), y (\frac{π}{2}) = 7

x^{2} - 41, 7 - 2 x

\int sin (θ) sin (3 θ) sin (5 θ) d θ

x, at x = 100

What is the derivative of (4/5 x^5) ?
The derivative of (4/5 x^5) is (1024x^4)/(625)
What is the first derivative of (4/5 x^5) ?
The first derivative of (4/5 x^5) is (1024x^4)/(625)