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Popular >

derivative of 0.5e^{x/3}-sin(x)

Solution

\frac{d}{d x} (0.5 e^{\frac{x}{3}} - sin (x))

Solution

0.16666 \dots e^{\frac{x}{3}} - cos (x)

Solution steps

\frac{d}{d x} (0.5 e^{\frac{x}{3}} - sin (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (0.5 e^{\frac{x}{3}}) - \frac{d}{d x} (sin (x))

\frac{d}{d x} (0.5 e^{\frac{x}{3}}) = 0.16666 \dots e^{\frac{x}{3}}

\frac{d}{d x} (sin (x)) = cos (x)

= 0.16666 \dots e^{\frac{x}{3}} - cos (x)

Popular Examples

integral from 0 to 4 of x-2sqrt(x)

\int_{0}^{4} x - 2 x d x

integral of-xsqrt(x-1)

\int - x x - 1 d x

limit as x approaches infinity of sin(arctan(x))

x \to \infty lim (sin (arctan (x)))

(\partial)/(\partial x)(xln(x^2+y^2))

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

(\partial)/(\partial x)(4x(5+y)^{-1})

\frac{\partial}{\partial x} (4 x (5 + y)^{- 1})

Frequently Asked Questions (FAQ)

What is the derivative of 0.5e^{x/3}-sin(x) ?
The derivative of 0.5e^{x/3}-sin(x) is 0.16666…e^{x/3}-cos(x)
What is the first derivative of 0.5e^{x/3}-sin(x) ?
The first derivative of 0.5e^{x/3}-sin(x) is 0.16666…e^{x/3}-cos(x)