What is the d/(df)(({Q}(f))k({Q}(f)-70)) ?

The d/(df)(({Q}(f))k({Q}(f)-70)) is k(2{Q}(f) d/(df)({Q}(f))-70 d/(df)({Q}(f)))

What is the first d/(df)(({Q}(f))k({Q}(f)-70)) ?

The first d/(df)(({Q}(f))k({Q}(f)-70)) is k(2{Q}(f) d/(df)({Q}(f))-70 d/(df)({Q}(f)))

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\frac{d}{df} ((Q (f)) k (Q (f) - 70))

k (2 Q (f) \frac{d}{df} (Q (f)) - 70 \frac{d}{df} (Q (f)))

Solution steps

\frac{d}{df} ((Q (f)) k (Q (f) - 70))

Take the constant out:

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

= k \frac{d}{df} (Q (f) (Q (f) - 70))

Apply the Product Rule:

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

f = Q (f), g = Q (f) - 70

= k (\frac{d}{df} (Q (f)) (Q (f) - 70) + \frac{d}{df} (Q (f) - 70) Q (f))

\frac{d}{df} (Q (f) - 70) = \frac{d}{df} (Q (f))

= k (\frac{d}{df} (Q (f)) (Q (f) - 70) + \frac{d}{df} (Q (f)) Q (f))

Expand

\frac{d}{df} (Q (f)) (Q (f) - 70) + \frac{d}{df} (Q (f)) Q (f) : 2 Q (f) \frac{d}{df} (Q (f)) - 70 \frac{d}{df} (Q (f))

= k (2 Q (f) \frac{d}{df} (Q (f)) - 70 \frac{d}{df} (Q (f)))

\frac{x + 5}{( x - 4 ) ( x + 3 )}

\frac{( x + h )}{2 ( x + h ) - 5}

(2 x + 1) ln (3)

\frac{( 100 - 94 cos ( x ) ) ^{2}}{4}

- \frac{6 x}{( x ^{2} + 9 ) ^{2}}

What is the d/(df)(({Q}(f))k({Q}(f)-70)) ?
The d/(df)(({Q}(f))k({Q}(f)-70)) is k(2{Q}(f) d/(df)({Q}(f))-70 d/(df)({Q}(f)))
What is the first d/(df)(({Q}(f))k({Q}(f)-70)) ?
The first d/(df)(({Q}(f))k({Q}(f)-70)) is k(2{Q}(f) d/(df)({Q}(f))-70 d/(df)({Q}(f)))