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Popular >

derivative of sqrt(x)-(1/2 ^x)

Solution

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

Solution

\frac{1}{2 x} + ln (2) (\frac{1}{2})^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} ((\frac{1}{2})^{x}) = - ln (2) (\frac{1}{2})^{x}

= \frac{1}{2 x} - (- ln (2) (\frac{1}{2})^{x})

Simplify

= \frac{1}{2 x} + ln (2) (\frac{1}{2})^{x}

Popular Examples

integral of cos^3(θ)+cos(θ)sin^2(θ)

\int cos^{3} (θ) + cos (θ) sin^{2} (θ) d θ

sum from n=1 to infinity of 5/(7^n)

n = 1 \sum \infty \frac{5}{7 ^{n}}

y(x+y+1)dx+2xydy=0

y (x + y + 1) d x + 2 x y d y = 0

integral from 0 to 4 of x/(x^2+1)

\int_{0}^{4} \frac{x}{x ^{2} + 1} d x

derivative of x^{4/5}-x^{2/3}

\frac{d}{d x} (x^{\frac{4}{5}} - x^{\frac{2}{3}})

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)-(1/2 ^x) ?
The derivative of sqrt(x)-(1/2 ^x) is 1/(2sqrt(x))+ln(2)(1/2)^x
What is the first derivative of sqrt(x)-(1/2 ^x) ?
The first derivative of sqrt(x)-(1/2 ^x) is 1/(2sqrt(x))+ln(2)(1/2)^x