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Popular >

derivative of f(xx^'(x))

Solution

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

Solution

(' + 1) x^{'} f (x) + \frac{d}{d x} (f (x)) x^{' + 1}

Solution steps

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

Simplify

f (x) x^{^{'}} (x) : x^{^{'} + 1} f (x)

= \frac{d}{d x} (x^{^{^{'}} + 1} f (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{^{'} + 1}, g = f (x)

= \frac{d}{d x} (x^{^{^{'}} + 1}) f (x) + \frac{d}{d x} (f (x)) x^{^{^{'}} + 1}

\frac{d}{d x} (x^{^{'} + 1}) = (^{'} + 1) x^{^{'}}

= (^{^{'}} + 1) x^{^{^{'}}} f (x) + \frac{d}{d x} (f (x)) x^{^{^{'}} + 1}

Popular Examples

(\partial)/(\partial x)(ln(8x^2+3y^2+3))

\frac{\partial}{\partial x} (ln (8 x^{2} + 3 y^{2} + 3))

integral of (10x^4-9x^2)/(2x^5-3x^3+14)

\int \frac{10 x ^{4} - 9 x ^{2}}{2 x ^{5} - 3 x ^{3} + 14} d x

y^{'''}+3y^{''}+3y^'+y=0

y^{^{'''}} + 3 y^{^{''}} + 3 y^{^{'}} + y = 0

(\partial)/(\partial x)((5y)/(x^3))

\frac{\partial}{\partial x} (\frac{5 y}{x ^{3}})

y^{''}-9y^'+18y=5sin(4t),y(0)=5,y^'(0)=2

y^{^{''}} - 9 y^{^{'}} + 18 y = 5 sin (4 t), y (0) = 5, y^{^{'}} (0) = 2

Frequently Asked Questions (FAQ)

What is the derivative of f(xx^'(x)) ?
The derivative of f(xx^'(x)) is ('+1)x^'{f}(x)+derivative of {f}(x)x^{'+1}
What is the first derivative of f(xx^'(x)) ?
The first derivative of f(xx^'(x)) is ('+1)x^'{f}(x)+derivative of {f}(x)x^{'+1}