What is the derivative of (2x^5-27/(x^4)) ?

The derivative of (2x^5-27/(x^4)) is (2(x^5+54))/(x^5)

What is the first derivative of (2x^5-27/(x^4)) ?

The first derivative of (2x^5-27/(x^4)) is (2(x^5+54))/(x^5)

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\frac{d}{d x} (\frac{2 x ^{5} - 27}{x ^{4}})

\frac{2 ( x ^{5} + 54 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{2 x ^{5} - 27}{x ^{4}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 2 x ^{5} - 27 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 2 x ^{5} - 27 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (2 x^{5} - 27) = 10 x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

= \frac{10 x ^{4} x ^{4} - 4 x ^{3} ( 2 x ^{5} - 27 )}{( x ^{4} ) ^{2}}

Simplify

\frac{10 x ^{4} x ^{4} - 4 x ^{3} ( 2 x ^{5} - 27 )}{( x ^{4} ) ^{2}} : \frac{2 ( x ^{5} + 54 )}{x ^{5}}

= \frac{2 ( x ^{5} + 54 )}{x ^{5}}

\int 30 (1 + x) d x

y^{^{''}} + 4 y = \frac{x}{x - 2}

\frac{\partial}{\partial x} ((x + y) \cdot e^{y^{2}})

2 cos (2 x)

f (x) = \frac{ln ( x ^{2} )}{x}

What is the derivative of (2x^5-27/(x^4)) ?
The derivative of (2x^5-27/(x^4)) is (2(x^5+54))/(x^5)
What is the first derivative of (2x^5-27/(x^4)) ?
The first derivative of (2x^5-27/(x^4)) is (2(x^5+54))/(x^5)