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Popular >

derivative of y=(x^4)/(f(x))

Solution

derivative of

y = \frac{x ^{4}}{f ( x )}

Solution

\frac{4 x ^{3} f ( x ) - \frac{df}{d x} x ^{4}}{f ( x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{4}}{f ( x )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{4} ) f ( x ) - \frac{df}{d x} x ^{4}}{f ( x ) ^{2}}

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

= \frac{4 x ^{3} f ( x ) - \frac{df}{d x} x ^{4}}{f ( x ) ^{2}}

Popular Examples

derivative of f(x)=3x^2-4x derivative of

f (x) = 3 x^{2} - 4 x

y^{''}+2y^'+26y=0,y(0)=4,y^'(0)=-2

y^{^{''}} + 2 y^{^{'}} + 26 y = 0, y (0) = 4, y^{^{'}} (0) = - 2

derivative of sqrt(x)*ln(x)

\frac{d}{d x} (x \cdot ln (x))

(\partial)/(\partial x)(x^{2+y^2})

\frac{\partial}{\partial x} (x^{2 + y^{2}})

integral of (15x^4)

\int (15 x^{4}) d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^4)/(f(x)) ?
The derivative of y=(x^4)/(f(x)) is (4x^3f(x)-\frac{df)/(dx)x^4}{f(x)^2}
What is the first derivative of y=(x^4)/(f(x)) ?
The first derivative of y=(x^4)/(f(x)) is (4x^3f(x)-\frac{df)/(dx)x^4}{f(x)^2}