What is the derivative of (x^4/(sqrt(x^5+3))) ?

The derivative of (x^4/(sqrt(x^5+3))) is (3x^8+24x^3)/(2(x^5+3)sqrt(x^5+3))

What is the first derivative of (x^4/(sqrt(x^5+3))) ?

The first derivative of (x^4/(sqrt(x^5+3))) is (3x^8+24x^3)/(2(x^5+3)sqrt(x^5+3))

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

\frac{3 x ^{8} + 24 x ^{3}}{2 ( x ^{5} + 3 ) x ^{5} + 3}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{4 x ^{3} x ^{5} + 3 - \frac{5 x ^{4}}{2 x ^{5} + 3} x ^{4}}{( x ^{5} + 3 ) ^{2}} : \frac{3 x ^{8} + 24 x ^{3}}{2 ( x ^{5} + 3 ) x ^{5} + 3}

= \frac{3 x ^{8} + 24 x ^{3}}{2 ( x ^{5} + 3 ) x ^{5} + 3}

\frac{\partial}{\partial y} (3 x + y)

\int \frac{23}{23 + e ^{x}} d x

\frac{\partial}{\partial x} (x y + ln (x + y))

\frac{d}{d x} (sin^{l n (x)} (3 x))

\int sin (a t) d t

What is the derivative of (x^4/(sqrt(x^5+3))) ?
The derivative of (x^4/(sqrt(x^5+3))) is (3x^8+24x^3)/(2(x^5+3)sqrt(x^5+3))
What is the first derivative of (x^4/(sqrt(x^5+3))) ?
The first derivative of (x^4/(sqrt(x^5+3))) is (3x^8+24x^3)/(2(x^5+3)sqrt(x^5+3))