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derivative of sin^2(x+2^{sin(x)})

Solution

\frac{d}{d x} (sin^{2} (x) + 2^{s i n (x)})

Solution

sin (2 x) + ln (2) \cdot 2^{s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (sin^{2} (x) + 2^{s i n (x)})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (sin^{2} (x)) + \frac{d}{d x} (2^{s i n (x)})

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

\frac{d}{d x} (2^{s i n (x)}) = ln (2) \cdot 2^{s i n (x)} cos (x)

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

Popular Examples

sum from n=1 to infinity of n/(n^2+1)

n = 1 \sum \infty \frac{n}{n ^{2} + 1}

derivative of x^{1/3}y^{2/3}

\frac{d}{d x} (x^{\frac{1}{3}} y^{\frac{2}{3}})

derivative of 1/2 x^2-x+1/6 x^3

\frac{d}{d x} (\frac{1}{2} x^{2} - x + \frac{1}{6} x^{3})

integral of x^2*sqrt(x)

\int x^{2} \cdot x d x

integral of x/((x+1)(x+2)(x+3)^2)

\int \frac{x}{( x + 1 ) ( x + 2 ) ( x + 3 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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