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Popular >

derivative of {f}(x(sqrt(x)))

Solution

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

Solution

x \frac{d}{d x} (f (x)) + \frac{f ( x )}{2 x}

Solution steps

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

Apply the Product Rule:

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

f = f (x), g = x

= \frac{d}{d x} (f (x)) x + \frac{d}{d x} (x) f (x)

\frac{d}{d x} (x) = \frac{1}{2 x}

= \frac{d}{d x} (f (x)) x + \frac{1}{2 x} f (x)

\frac{1}{2 x} f (x) = \frac{f ( x )}{2 x}

= x \frac{d}{d x} (f (x)) + \frac{f ( x )}{2 x}

Popular Examples

derivative of 3x^2-2x+7

\frac{d}{d x} (3 x^{2} - 2 x + 7)

limit as x approaches 2 of (x+2)^6(3x^2)

x \to 2 lim ((x + 2)^{6} (3 x^{2}))

y^{''}+9y=t^2e^3t+6

y^{^{''}} + 9 y = t^{2} e^{3} t + 6

inverse oflaplace 1/((s-3)(s+1))inverse laplace

\frac{1}{( s - 3 ) ( s + 1 )}

integral of (3x-y)/9

\int \frac{3 x - y}{9} d y

Frequently Asked Questions (FAQ)

What is the derivative of {f}(x(sqrt(x))) ?
The derivative of {f}(x(sqrt(x))) is sqrt(x) derivative of {f}(x)+({f}(x))/(2sqrt(x))
What is the first derivative of {f}(x(sqrt(x))) ?
The first derivative of {f}(x(sqrt(x))) is sqrt(x) derivative of {f}(x)+({f}(x))/(2sqrt(x))