# left f(x)=2^(sin(x)) Find f'(x)

Question
left $$f(x)=2^(sin(x))$$
Find f'(x)

2021-02-10
To compute the derivative of the given function (involving exponentials)
Step 2
Here ,we have used chain rule: If h(x)= p(q(x)), then h'(x) = p'(q) times q'(x)
Write $$f(x)=2^(u(x)),u(x)=sinx$$
by chain rule
$$f'(x)=(2^u)$$(derivative wrt u)*u'(x)
$$=2^uIn(2)cosx$$
$$=(In2)2^(sinx)(cosx)$$

### Relevant Questions

The parabola shown is the graph of $$f(x) = Ax^{2}\ +\ 2x\ +\ C.$$
The x-intercepts of the graph are at $$-4\ and\ -3.$$ Find the exact value of the y-intercept and the coordinates of the vertex of the graph (expressed in terms of rational numbers and radicals).
Use the rational zeros theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers.
Find the real zeros of $$f(x) = 5x^{3}\ -\ x^{2}\ +\ 5x\ -\ 1$$
Find the rational zeros and then other zeros of the polynomial function $$f(x) = x^{3}\ -\ 17x^{2}\ +\ 55x\ +\ 25,$$
that is, solve $$f(x) = 0$$
Factor $$f(x)$$ into linear factors
Find and solve the exact value of each of the following under the given conditions $$\tan\ \alpha =\ -\frac{7}{24},\ \alpha$$ lies in quadrant 2,
$$\cos\ \beta = \frac{3}{4},\ \beta$$ lies in quadrant 1
a. $$\sin(\alpha\ +\ \beta)$$
b. $$\cos(\alpha\ +\ \beta)$$
c. $$\tan (\alpha\ +\ \beta)$$
Use rational exponents to write a single radical expression $$\left(\sqrt[3]{x^{2}y^{5}}\right)^{12}$$
a) Find the rational zeros and then the other zeros of the polynomial function $$\displaystyle{\left({x}\right)}={x}^{3}-{4}{x}^{2}+{2}{x}+{4},\ \tet{that is, solve}\ \displaystyle f{{\left({x}\right)}}={0}.$$
b) Factor $$f(x)$$ into linear factors.
(a) find the rational zeros and then the other zeros of the polynomial function $$(x)=x3-4x2+2x+4$$, that is, solve
$$f(x)=0.$$ (type an exact answer, using radicals as needed. Simplify your answer. Use a comma to separate answers as needed.)
Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}\ -\ {7}{x}^{{{2}}}\ +\ {2}{x}\ +\ {3}$$ given that 3 is a zero.
$$f(x)=2^(x-3)-3$$
Graph each polynomial function. $$\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{5}{x}^{{{2}}}+{6}$$