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Popular >

derivative of sqrt({f)(x}-4x+1)

Solution

\frac{d}{d x} (f (x) - 4 x + 1)

Solution

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

Solution steps

\frac{d}{d x} (f (x) - 4 x + 1)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (f (x)) - \frac{d}{d x} (4 x) + \frac{d}{d x} (1)

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

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

\frac{d}{d x} (1) = 0

= \frac{\frac{d}{d x} ( f ( x ) )}{2 f ( x )} - 4 + 0

Simplify

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

Popular Examples

sum from n=1 to infinity of (10/11)^n

n = 1 \sum \infty (\frac{10}{11})^{n}

derivative of f(x)=-x-1/x derivative of

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

derivative of e^{(x-1})

\frac{d}{d x} (e^{(x - 1)})

derivative of (8x^2-40x+32/(3x^{1/3)})

\frac{d}{d x} (\frac{8 x ^{2} - 40 x + 32}{3 x ^{\frac{1}{3}}})

derivative of (x^2/(x^2+2x-15))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 2 x - 15})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt({f)(x}-4x+1) ?
The derivative of sqrt({f)(x}-4x+1) is (derivative of {f}(x))/(2sqrt({f)(x))}-4
What is the first derivative of sqrt({f)(x}-4x+1) ?
The first derivative of sqrt({f)(x}-4x+1) is (derivative of {f}(x))/(2sqrt({f)(x))}-4