What is the derivative of (2x-e^2x^{sin(2x)}) ?

The derivative of (2x-e^2x^{sin(2x)}) is (2cos(2x)ln(2x-e^2x)+(sin(2x))/x)(2x-e^2x)^{sin(2x)}

What is the first derivative of (2x-e^2x^{sin(2x)}) ?

The first derivative of (2x-e^2x^{sin(2x)}) is (2cos(2x)ln(2x-e^2x)+(sin(2x))/x)(2x-e^2x)^{sin(2x)}

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\frac{d}{d x} ((2 x - e^{2} x)^{s i n (2 x)})

(2 cos (2 x) ln (2 x - e^{2} x) + \frac{sin ( 2 x )}{x}) (2 x - e^{2} x)^{s i n (2 x)}

Solution steps

\frac{d}{d x} ((2 x - e^{2} x)^{s i n (2 x)})

Apply exponent rule:

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

(2 x - e^{2} x)^{s i n (2 x)} = e^{s i n (2 x) l n (2 x - e^{2} x)}

= \frac{d}{d x} (e^{s i n (2 x) l n (2 x - e^{2} x)})

Apply the chain rule:

e^{s i n (2 x) l n (2 x - e^{2} x)} \frac{d}{d x} (sin (2 x) ln (2 x - e^{2} x))

= e^{s i n (2 x) l n (2 x - e^{2} x)} \frac{d}{d x} (sin (2 x) ln (2 x - e^{2} x))

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

= e^{s i n (2 x) l n (2 x - e^{2} x)} (2 cos (2 x) ln (2 x - e^{2} x) + \frac{sin ( 2 x )}{x})

e^{s i n (2 x) l n (2 x - e^{2} x)} = (2 x - e^{2} x)^{s i n (2 x)}

= (2 cos (2 x) ln (2 x - e^{2} x) + \frac{sin ( 2 x )}{x}) (2 x - e^{2} x)^{s i n (2 x)}

\int \frac{x}{t ^{2}} d t

4 x - 8

\frac{d}{d s} (\frac{s}{s ^{2} + 1})

14450 e^{- 0.167 t}

(x^{3} + 4 x) (3 x^{2} + 2 x - 5)

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