What is the d/(dp)((h)(p(1+3p)^5)) ?

The d/(dp)((h)(p(1+3p)^5)) is h((1+3p)^5+15p(1+3p)^4)

What is the first d/(dp)((h)(p(1+3p)^5)) ?

The first d/(dp)((h)(p(1+3p)^5)) is h((1+3p)^5+15p(1+3p)^4)

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\frac{d}{d p} ((h) (p (1 + 3 p)^{5}))

h ((1 + 3 p)^{5} + 15 p (1 + 3 p)^{4})

Solution steps

\frac{d}{d p} ((h) (p (1 + 3 p)^{5}))

Treat

h

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= h \frac{d}{d p} (p (1 + 3 p)^{5})

Apply the Product Rule:

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

f = p, g = (1 + 3 p)^{5}

= h (\frac{d p}{d p} (1 + 3 p)^{5} + \frac{d}{d p} ((1 + 3 p)^{5}) p)

\frac{d p}{d p} = 1

\frac{d}{d p} ((1 + 3 p)^{5}) = 15 (1 + 3 p)^{4}

= h (1 \cdot (1 + 3 p)^{5} + 15 (1 + 3 p)^{4} p)

Simplify

= h ((1 + 3 p)^{5} + 15 p (1 + 3 p)^{4})

(\frac{2 ( i - 1 )}{n})^{2}

(x y + y^{2}) d x + x^{2} d y

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

\frac{( 1 - 2 y ) ^{3}}{3}

\frac{3 ( t ^{2} + 20 t )}{10 + t}

What is the d/(dp)((h)(p(1+3p)^5)) ?
The d/(dp)((h)(p(1+3p)^5)) is h((1+3p)^5+15p(1+3p)^4)
What is the first d/(dp)((h)(p(1+3p)^5)) ?
The first d/(dp)((h)(p(1+3p)^5)) is h((1+3p)^5+15p(1+3p)^4)