en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of 5^x+5cos((5x/2))

Solution

\frac{d}{d x} (5^{x} + 5 cos (\frac{5 x}{2}))

Solution

5^{x} ln (5) - \frac{25}{2} sin (\frac{5 x}{2})

Solution steps

\frac{d}{d x} (5^{x} + 5 cos (\frac{5 x}{2}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5^{x}) + \frac{d}{d x} (5 cos (\frac{5 x}{2}))

\frac{d}{d x} (5^{x}) = 5^{x} ln (5)

\frac{d}{d x} (5 cos (\frac{5 x}{2})) = - \frac{25}{2} sin (\frac{5 x}{2})

= 5^{x} ln (5) - \frac{25}{2} sin (\frac{5 x}{2})

Popular Examples

integral of (5+t+t^2)/(sqrt(t))

\int \frac{5 + t + t ^{2}}{t} d t

x(dy)/(dx)=y-1/y

x \frac{d y}{d x} = y - \frac{1}{y}

limit as x approaches-5-of (|x+5|)/(x+5)

x \to - 5 - lim (\frac{∣ x + 5 ∣}{x + 5})

integral of x^5e^{-x^6}

\int x^{5} e^{- x^{6}} d x

sqrt(x)+sqrt(y)((dy)/(dx))=0

x + y (\frac{d y}{d x}) = 0

Frequently Asked Questions (FAQ)

What is the derivative of 5^x+5cos((5x/2)) ?
The derivative of 5^x+5cos((5x/2)) is 5^xln(5)-25/2 sin((5x)/2)
What is the first derivative of 5^x+5cos((5x/2)) ?
The first derivative of 5^x+5cos((5x/2)) is 5^xln(5)-25/2 sin((5x)/2)