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

The derivative of (5^{x^3})/(4x^2) is (5^{x^3}(3ln(5)x^3-2))/(4x^3)

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

The first derivative of (5^{x^3})/(4x^2) is (5^{x^3}(3ln(5)x^3-2))/(4x^3)

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derivative of

\frac{5 ^{x^{3}}}{4 x ^{2}}

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

Solution steps

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

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{5 ^{x^{3}}}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{1}{4} \cdot \frac{\frac{d}{d x} ( 5 ^{x^{3}} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) 5 ^{x^{3}}}{( x ^{2} ) ^{2}}

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

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

= \frac{1}{4} \cdot \frac{3 ln ( 5 ) \cdot 5 ^{x^{3}} x ^{2} x ^{2} - 2 x \cdot 5 ^{x^{3}}}{( x ^{2} ) ^{2}}

Simplify

\frac{1}{4} \cdot \frac{3 ln ( 5 ) \cdot 5 ^{x^{3}} x ^{2} x ^{2} - 2 x \cdot 5 ^{x^{3}}}{( x ^{2} ) ^{2}} : \frac{5 ^{x^{3}} ( 3 ln ( 5 ) x ^{3} - 2 )}{4 x ^{3}}

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

y = ln (x - 9)

\int_{0}^{1} \frac{2 x}{1 + x ^{2}} d x

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

\int 4 x 4 - x^{2} d x

\frac{\partial}{\partial x} (x y + yz + z x - 3)

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