What is the derivative of (e^{(7x/4})/(1-9x^2)) ?

The derivative of (e^{(7x/4})/(1-9x^2)) is (7/4 e^{(7x)/4}(1-9x^2)+18e^{(7x)/4}x)/((1-9x^2)^2)

What is the first derivative of (e^{(7x/4})/(1-9x^2)) ?

The first derivative of (e^{(7x/4})/(1-9x^2)) is (7/4 e^{(7x)/4}(1-9x^2)+18e^{(7x)/4}x)/((1-9x^2)^2)

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\frac{d}{d x} (\frac{e ^{\frac{7 x}{4}}}{1 - 9 x ^{2}})

\frac{\frac{7}{4} e ^{\frac{7 x}{4}} ( 1 - 9 x ^{2} ) + 18 e ^{\frac{7 x}{4}} x}{( 1 - 9 x ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{e ^{\frac{7 x}{4}}}{1 - 9 x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( e ^{\frac{7 x}{4}} ) ( 1 - 9 x ^{2} ) - \frac{d}{d x} ( 1 - 9 x ^{2} ) e ^{\frac{7 x}{4}}}{( 1 - 9 x ^{2} ) ^{2}}

\frac{d}{d x} (e^{\frac{7 x}{4}}) = e^{\frac{7 x}{4}} \frac{7}{4}

\frac{d}{d x} (1 - 9 x^{2}) = - 18 x

= \frac{e ^{\frac{7 x}{4}} \frac{7}{4} ( 1 - 9 x ^{2} ) - ( - 18 x ) e ^{\frac{7 x}{4}}}{( 1 - 9 x ^{2} ) ^{2}}

Simplify

= \frac{\frac{7}{4} e ^{\frac{7 x}{4}} ( 1 - 9 x ^{2} ) + 18 e ^{\frac{7 x}{4}} x}{( 1 - 9 x ^{2} ) ^{2}}

\int_{0}^{2} - 6 x^{3} x^{2} + 4 d x

\frac{d}{d x} (1 + x + 5 x^{2})

\int_{- 2}^{1} 2 - x^{2} - x d x

(x^{9} - 1)^{3}

y = 3 x, y = 2 x - 18, y = 0

What is the derivative of (e^{(7x/4})/(1-9x^2)) ?
The derivative of (e^{(7x/4})/(1-9x^2)) is (7/4 e^{(7x)/4}(1-9x^2)+18e^{(7x)/4}x)/((1-9x^2)^2)
What is the first derivative of (e^{(7x/4})/(1-9x^2)) ?
The first derivative of (e^{(7x/4})/(1-9x^2)) is (7/4 e^{(7x)/4}(1-9x^2)+18e^{(7x)/4}x)/((1-9x^2)^2)