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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\frac{d}{d x} (\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 y^{^{'}} = \frac{7}{x}

(1 + e^{2 x}) y^{2} d y = e^{x} d x, y (0) = 0

\int 2 x - \frac{1}{1 + x ^{2}} d x

f (x) = 5 - ∣ x - 5 ∣

\int \frac{x ^{2} + x + 1}{x ^{2} - x} d x

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)