What is the d/(dm)(c^{im}) ?

The d/(dm)(c^{im}) is ic^{im}ln(c)

What is the first d/(dm)(c^{im}) ?

The first d/(dm)(c^{im}) is ic^{im}ln(c)

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\frac{d}{d m} (c^{im})

i c^{im} ln (c)

Solution steps

\frac{d}{d m} (c^{im})

Treat

i, c

as a constant

Apply exponent rule:

a^{b} = e^{b l n (a)}

c^{im} = e^{im l n (c)}

= \frac{d}{d m} (e^{im l n (c)})

Apply the chain rule:

e^{im l n (c)} \frac{d}{d m} (im ln (c))

= e^{im l n (c)} \frac{d}{d m} (im ln (c))

\frac{d}{d m} (im ln (c)) = i ln (c)

= e^{im l n (c)} i ln (c)

e^{im l n (c)} = c^{im}

= i c^{im} ln (c)

\frac{d}{d x} (5 x^{3} + 2 x^{2} + 6 x + 10)

g (x) = \frac{1}{5 x ^{2} + 3 x}

x \to \infty lim (x^{- 7})

\frac{d}{d x} (sin (cos (x^{2} + 3 x)))

\frac{d}{d x} (- sec (x) + 2 sec^{3} (x))