What is the d/(dy)((q)(q^{0.3}+y^{0.3})) ?

The d/(dy)((q)(q^{0.3}+y^{0.3})) is y^{0.3}(dq)/(dy)+1.3(dq)/(dy)q^{0.3}+(0.3q)/(y^{0.7)}

What is the first d/(dy)((q)(q^{0.3}+y^{0.3})) ?

The first d/(dy)((q)(q^{0.3}+y^{0.3})) is y^{0.3}(dq)/(dy)+1.3(dq)/(dy)q^{0.3}+(0.3q)/(y^{0.7)}

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\frac{d}{d y} ((q) (q^{0.3} + y^{0.3}))

y^{0.3} \frac{d q}{d y} + 1.3 \frac{d q}{d y} q^{0.3} + \frac{0.3 q}{y ^{0.7}}

Solution steps

\frac{d}{d y} ((q) (q^{0.3} + y^{0.3}))

Apply the Product Rule:

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

f = q, g = q^{0.3} + y^{0.3}

= \frac{d q}{d y} (q^{0.3} + y^{0.3}) + \frac{d}{d y} (q^{0.3} + y^{0.3}) q

\frac{d}{d y} (q^{0.3} + y^{0.3}) = \frac{0.3 \frac{d q}{d y}}{q ^{0.7}} + \frac{0.3}{y ^{0.7}}

= \frac{d q}{d y} (q^{0.3} + y^{0.3}) + (\frac{0.3 \frac{d q}{d y}}{q ^{0.7}} + \frac{0.3}{y ^{0.7}}) q

Simplify

\frac{d q}{d y} (q^{0.3} + y^{0.3}) + (\frac{0.3 \frac{d q}{d y}}{q ^{0.7}} + \frac{0.3}{y ^{0.7}}) q : y^{0.3} \frac{d q}{d y} + 1.3 \frac{d q}{d y} q^{0.3} + \frac{0.3 q}{y ^{0.7}}

= y^{0.3} \frac{d q}{d y} + 1.3 \frac{d q}{d y} q^{0.3} + \frac{0.3 q}{y ^{0.7}}

\frac{( s ( s + 100 ) ^{2} ( s + w ^{2} ) )}{s ^{2} + w}

(1 - \frac{x}{2}) (5 + x)^{6}

(- a - b - c)^{2} + 4 ab c

(2 x d x - 4 x^{3}) d x - (2 y d y + x^{2}) d y

(x - 2) (x - \frac{1}{2}) (x + 4)

What is the d/(dy)((q)(q^{0.3}+y^{0.3})) ?
The d/(dy)((q)(q^{0.3}+y^{0.3})) is y^{0.3}(dq)/(dy)+1.3(dq)/(dy)q^{0.3}+(0.3q)/(y^{0.7)}
What is the first d/(dy)((q)(q^{0.3}+y^{0.3})) ?
The first d/(dy)((q)(q^{0.3}+y^{0.3})) is y^{0.3}(dq)/(dy)+1.3(dq)/(dy)q^{0.3}+(0.3q)/(y^{0.7)}