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Popular >

d/(dq)(({R}(q))((q^4+1)^5))

Solution

\frac{d}{d q} ((R (q)) ((q^{4} + 1)^{5}))

Solution

\frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)

Solution steps

\frac{d}{d q} ((R (q)) ((q^{4} + 1)^{5}))

Apply the Product Rule:

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

f = R (q), g = (q^{4} + 1)^{5}

= \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + \frac{d}{d q} ((q^{4} + 1)^{5}) R (q)

\frac{d}{d q} ((q^{4} + 1)^{5}) = 20 q^{3} (q^{4} + 1)^{4}

= \frac{d}{d q} (R (q)) (q^{4} + 1)^{5} + 20 q^{3} (q^{4} + 1)^{4} R (q)

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Frequently Asked Questions (FAQ)

What is the d/(dq)(({R}(q))((q^4+1)^5)) ?
The d/(dq)(({R}(q))((q^4+1)^5)) is d/(dq)({R}(q))(q^4+1)^5+20q^3(q^4+1)^4{R}(q)
What is the first d/(dq)(({R}(q))((q^4+1)^5)) ?
The first d/(dq)(({R}(q))((q^4+1)^5)) is d/(dq)({R}(q))(q^4+1)^5+20q^3(q^4+1)^4{R}(q)