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Popular Calculus >

derivative of e^p(p+sqrt(p))

Solution

derivative of

e^{p} (p + p)

Solution

e^{p} (p + p) + (1 + \frac{1}{2 p}) e^{p}

Solution steps

\frac{d}{d p} (e^{p} (p + p))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{p}, g = p + p

= \frac{d}{d p} (e^{p}) (p + p) + \frac{d}{d p} (p + p) e^{p}

\frac{d}{d p} (e^{p}) = e^{p}

\frac{d}{d p} (p + p) = 1 + \frac{1}{2 p}

= e^{p} (p + p) + (1 + \frac{1}{2 p}) e^{p}

Graph

Popular Examples

integral of t/((t+1)^4)

\int \frac{t}{( t + 1 ) ^{4}} d t

x*ln(x)=y(1+sqrt(3+y^2))y^'(x),y(1)=1

x \cdot ln (x) = y (1 + 3 + y^{2}) y^{^{'}} (x), y (1) = 1

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

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

integral of 3-x

\int 3 - x d x

laplacetransform 15t^4e^{4t}+10

l a pl a ce t r an s f or m 15 t^{4} e^{4 t} + 10

Frequently Asked Questions (FAQ)

What is the derivative of e^p(p+sqrt(p)) ?
The derivative of e^p(p+sqrt(p)) is e^p(p+sqrt(p))+(1+1/(2sqrt(p)))e^p
What is the first derivative of e^p(p+sqrt(p)) ?
The first derivative of e^p(p+sqrt(p)) is e^p(p+sqrt(p))+(1+1/(2sqrt(p)))e^p