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Popular >

derivative of y=(x^7)/(f(x))

Solution

derivative of

y = \frac{x ^{7}}{f ( x )}

Solution

\frac{7 x ^{6} f ( x ) - \frac{df}{d x} x ^{7}}{f ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{7}}{f ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{7} ) f ( x ) - \frac{df}{d x} x ^{7}}{f ( x ) ^{2}}

\frac{d}{d x} (x^{7}) = 7 x^{6}

= \frac{7 x ^{6} f ( x ) - \frac{df}{d x} x ^{7}}{f ( x ) ^{2}}

Popular Examples

derivative of x^7e^{9x}

\frac{d}{d x} (x^{7} e^{9 x})

tangent of f(x)=(16x)/(x^2+16)tangent of

f (x) = \frac{16 x}{x ^{2} + 16}

limit as h approaches 0 of ((pi+h)+1)/h

h \to 0 lim (\frac{( π + h ) + 1}{h})

derivative of ((x^2-3x)/(sqrt(4x+1)))

\frac{d}{d x} (\frac{( x ^{2} - 3 x )}{4 x + 1})

area x,0,3 area

x, 0, 3

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^7)/(f(x)) ?
The derivative of y=(x^7)/(f(x)) is (7x^6f(x)-\frac{df)/(dx)x^7}{f(x)^2}
What is the first derivative of y=(x^7)/(f(x)) ?
The first derivative of y=(x^7)/(f(x)) is (7x^6f(x)-\frac{df)/(dx)x^7}{f(x)^2}