What is the derivative of 4^{3sin(x-e^x}) ?

The derivative of 4^{3sin(x-e^x}) is ln(2)*2^{2(3sin(x)-e^x)+1}(3cos(x)-e^x)

What is the first derivative of 4^{3sin(x-e^x}) ?

The first derivative of 4^{3sin(x-e^x}) is ln(2)*2^{2(3sin(x)-e^x)+1}(3cos(x)-e^x)

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\frac{d}{d x} (4^{3 s i n (x) - e^{x}})

ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

Solution steps

\frac{d}{d x} (4^{3 s i n (x) - e^{x}})

Apply exponent rule:

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

4^{3 s i n (x) - e^{x}} = e^{(3 s i n (x) - e^{x}) l n (4)}

= \frac{d}{d x} (e^{(3 s i n (x) - e^{x}) l n (4)})

Apply the chain rule:

e^{(3 s i n (x) - e^{x}) l n (4)} \frac{d}{d x} ((3 sin (x) - e^{x}) ln (4))

= e^{(3 s i n (x) - e^{x}) l n (4)} \frac{d}{d x} ((3 sin (x) - e^{x}) ln (4))

\frac{d}{d x} ((3 sin (x) - e^{x}) ln (4)) = 2 ln (2) (3 cos (x) - e^{x})

= e^{(3 s i n (x) - e^{x}) l n (4)} \cdot 2 ln (2) (3 cos (x) - e^{x})

Simplify

e^{(3 s i n (x) - e^{x}) l n (4)} \cdot 2 ln (2) (3 cos (x) - e^{x}) : ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

= ln (2) \cdot 2^{2 (3 s i n (x) - e^{x}) + 1} (3 cos (x) - e^{x})

What is the derivative of 4^{3sin(x-e^x}) ?
The derivative of 4^{3sin(x-e^x}) is ln(2)*2^{2(3sin(x)-e^x)+1}(3cos(x)-e^x)
What is the first derivative of 4^{3sin(x-e^x}) ?
The first derivative of 4^{3sin(x-e^x}) is ln(2)*2^{2(3sin(x)-e^x)+1}(3cos(x)-e^x)