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Popular >

derivative of a^x+sin(x+sqrt(x))

Solution

\frac{d}{d x} (a^{x} + sin (x) + x)

Solution

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

Solution steps

\frac{d}{d x} (a^{x} + sin (x) + x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a^{x}) + \frac{d}{d x} (sin (x)) + \frac{d}{d x} (x)

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

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

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

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

Graph

Popular Examples

integral of x^2sqrt(5-x^2)

\int x^{2} 5 - x^{2} d x

(\partial)/(\partial x)(x^9y^7-x^8y^6)

\frac{\partial}{\partial x} (x^{9} y^{7} - x^{8} y^{6})

derivative of e^{3x+4}

\frac{d}{d x} (e^{3 x + 4})

derivative of sqrt(6+x)

\frac{d}{d x} (6 + x)

limit as x approaches 2 of g(x)

x \to 2 lim (g (x))

Frequently Asked Questions (FAQ)

What is the derivative of a^x+sin(x+sqrt(x)) ?
The derivative of a^x+sin(x+sqrt(x)) is a^xln(a)+cos(x)+1/(2sqrt(x))
What is the first derivative of a^x+sin(x+sqrt(x)) ?
The first derivative of a^x+sin(x+sqrt(x)) is a^xln(a)+cos(x)+1/(2sqrt(x))