What is the derivative of f(x)=x^8sqrt(5-3x) ?

The derivative of f(x)=x^8sqrt(5-3x) is (-51x^8+80x^7)/(2sqrt(5-3x))

What is the first derivative of f(x)=x^8sqrt(5-3x) ?

The first derivative of f(x)=x^8sqrt(5-3x) is (-51x^8+80x^7)/(2sqrt(5-3x))

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derivative

\frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

Solution steps

\frac{d}{d x} (x^{8} 5 - 3 x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{8}, g = 5 - 3 x

= \frac{d}{d x} (x^{8}) 5 - 3 x + \frac{d}{d x} (5 - 3 x) x^{8}

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

\frac{d}{d x} (5 - 3 x) = - \frac{3}{2 5 - 3 x}

= 8 x^{7} 5 - 3 x + (- \frac{3}{2 5 - 3 x}) x^{8}

Simplify

8 x^{7} 5 - 3 x + (- \frac{3}{2 5 - 3 x}) x^{8} : \frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

= \frac{- 51 x ^{8} + 80 x ^{7}}{2 5 - 3 x}

What is the derivative of f(x)=x^8sqrt(5-3x) ?
The derivative of f(x)=x^8sqrt(5-3x) is (-51x^8+80x^7)/(2sqrt(5-3x))
What is the first derivative of f(x)=x^8sqrt(5-3x) ?
The first derivative of f(x)=x^8sqrt(5-3x) is (-51x^8+80x^7)/(2sqrt(5-3x))