What is the derivative of (3x^4/((2-x^5)^3)) ?

The derivative of (3x^4/((2-x^5)^3)) is (3x^3(11x^5+8))/((2-x^5)^4)

What is the first derivative of (3x^4/((2-x^5)^3)) ?

The first derivative of (3x^4/((2-x^5)^3)) is (3x^3(11x^5+8))/((2-x^5)^4)

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\frac{d}{d x} (\frac{3 x ^{4}}{( 2 - x ^{5} ) ^{3}})

\frac{3 x ^{3} ( 11 x ^{5} + 8 )}{( 2 - x ^{5} ) ^{4}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{4}}{( 2 - x ^{5} ) ^{3}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{4} ) ( 2 - x ^{5} ) ^{3} - \frac{d}{d x} ( ( 2 - x ^{5} ) ^{3} ) x ^{4}}{( ( 2 - x ^{5} ) ^{3} ) ^{2}}

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

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

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

Simplify

3 \cdot \frac{4 x ^{3} ( 2 - x ^{5} ) ^{3} - ( - 15 x ^{4} ( 2 - x ^{5} ) ^{2} ) x ^{4}}{( ( 2 - x ^{5} ) ^{3} ) ^{2}} : \frac{3 x ^{3} ( 11 x ^{5} + 8 )}{( 2 - x ^{5} ) ^{4}}

= \frac{3 x ^{3} ( 11 x ^{5} + 8 )}{( 2 - x ^{5} ) ^{4}}

\frac{d}{d x} (5 x^{2})

n = 0 \sum \infty tan (\frac{1}{n})

\int \frac{1}{( e ^{x} + e ^{- x} )} d x

x \to 10 lim (3)

x \to 5 lim (x^{2} - 5 x)

What is the derivative of (3x^4/((2-x^5)^3)) ?
The derivative of (3x^4/((2-x^5)^3)) is (3x^3(11x^5+8))/((2-x^5)^4)
What is the first derivative of (3x^4/((2-x^5)^3)) ?
The first derivative of (3x^4/((2-x^5)^3)) is (3x^3(11x^5+8))/((2-x^5)^4)