What is the derivative of f(x)=(9(5^x))/(x^5) ?

The derivative of f(x)=(9(5^x))/(x^5) is (9*5^x(ln(5)x-5))/(x^6)

What is the first derivative of f(x)=(9(5^x))/(x^5) ?

The first derivative of f(x)=(9(5^x))/(x^5) is (9*5^x(ln(5)x-5))/(x^6)

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derivative of

f (x) = \frac{9 ( 5 ^{x} )}{x ^{5}}

\frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

Solution steps

\frac{d}{d x} (\frac{9 \cdot 5 ^{x}}{x ^{5}})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{5 ^{x}}{x ^{5}})

Apply the Quotient Rule:

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

= 9 \cdot \frac{\frac{d}{d x} ( 5 ^{x} ) x ^{5} - \frac{d}{d x} ( x ^{5} ) 5 ^{x}}{( x ^{5} ) ^{2}}

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

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

= 9 \cdot \frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}}

Simplify

9 \cdot \frac{5 ^{x} ln ( 5 ) x ^{5} - 5 x ^{4} \cdot 5 ^{x}}{( x ^{5} ) ^{2}} : \frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

= \frac{9 \cdot 5 ^{x} ( ln ( 5 ) x - 5 )}{x ^{6}}

\int lo g_{x} (x) d x

\int \frac{5 x ^{2} - 3}{x ( x ^{2} - 1 )} d x

f (x) = \frac{4 x ^{2} + 8 x + 8}{x}

\frac{\partial}{\partial y} (x e^{x})

\int (tan^{2} (x) + tan^{4} (x)) d x

What is the derivative of f(x)=(9(5^x))/(x^5) ?
The derivative of f(x)=(9(5^x))/(x^5) is (9*5^x(ln(5)x-5))/(x^6)
What is the first derivative of f(x)=(9(5^x))/(x^5) ?
The first derivative of f(x)=(9(5^x))/(x^5) is (9*5^x(ln(5)x-5))/(x^6)