What is the d/(dz)((w)(3z^7-7z^3+21z^2)) ?

The d/(dz)((w)(3z^7-7z^3+21z^2)) is w(21z^6-21z^2+42z)

What is the first d/(dz)((w)(3z^7-7z^3+21z^2)) ?

The first d/(dz)((w)(3z^7-7z^3+21z^2)) is w(21z^6-21z^2+42z)

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\frac{d}{d z} ((w) (3 z^{7} - 7 z^{3} + 21 z^{2}))

w (21 z^{6} - 21 z^{2} + 42 z)

Solution steps

\frac{d}{d z} ((w) (3 z^{7} - 7 z^{3} + 21 z^{2}))

Treat

w

as a constant

Take the constant out:

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

= w \frac{d}{d z} (3 z^{7} - 7 z^{3} + 21 z^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= w (\frac{d}{d z} (3 z^{7}) - \frac{d}{d z} (7 z^{3}) + \frac{d}{d z} (21 z^{2}))

\frac{d}{d z} (3 z^{7}) = 21 z^{6}

\frac{d}{d z} (7 z^{3}) = 21 z^{2}

\frac{d}{d z} (21 z^{2}) = 42 z

= w (21 z^{6} - 21 z^{2} + 42 z)

e^{x (x - 9)}

\frac{- 8 x sin ( x ) - 8 cos ( x )}{( cos ( x ) + 4 x ) ^{2}}

(1 + x)^{4} \cdot e^{x}

64 sin (θ) + 64 cos (θ) sin (θ)

(2 e + 12)^{2}

What is the d/(dz)((w)(3z^7-7z^3+21z^2)) ?
The d/(dz)((w)(3z^7-7z^3+21z^2)) is w(21z^6-21z^2+42z)
What is the first d/(dz)((w)(3z^7-7z^3+21z^2)) ?
The first d/(dz)((w)(3z^7-7z^3+21z^2)) is w(21z^6-21z^2+42z)