What is the derivative of (4x^5-15/(x^4)) ?

The derivative of (4x^5-15/(x^4)) is (4(x^5+15))/(x^5)

What is the first derivative of (4x^5-15/(x^4)) ?

The first derivative of (4x^5-15/(x^4)) is (4(x^5+15))/(x^5)

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\frac{d}{d x} (\frac{4 x ^{5} - 15}{x ^{4}})

\frac{4 ( x ^{5} + 15 )}{x ^{5}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{5} - 15}{x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{5} - 15 ) x ^{4} - \frac{d}{d x} ( x ^{4} ) ( 4 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

\frac{d}{d x} (4 x^{5} - 15) = 20 x^{4}

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

= \frac{20 x ^{4} x ^{4} - 4 x ^{3} ( 4 x ^{5} - 15 )}{( x ^{4} ) ^{2}}

Simplify

\frac{20 x ^{4} x ^{4} - 4 x ^{3} ( 4 x ^{5} - 15 )}{( x ^{4} ) ^{2}} : \frac{4 ( x ^{5} + 15 )}{x ^{5}}

= \frac{4 ( x ^{5} + 15 )}{x ^{5}}

y^{^{'}} = - \frac{y}{3}

\frac{d}{d x} (\frac{1}{1 + x ^{3}})

\int \frac{x ^{2} - x + 24}{x ^{3} + 6 x} d x

y = x - 3 x^{2}, (3, - 24)

f (t) = e^{8 t s i n (2 t)}

What is the derivative of (4x^5-15/(x^4)) ?
The derivative of (4x^5-15/(x^4)) is (4(x^5+15))/(x^5)
What is the first derivative of (4x^5-15/(x^4)) ?
The first derivative of (4x^5-15/(x^4)) is (4(x^5+15))/(x^5)