Application of ...

Let $$f'(\sin { x } )<0$$ and $$f''(\sin { x } )>0>\forall x\in \left( 0,\cfrac { \pi  }{ 2 }  \right) $$ and $$g(x)=f'(\sin { x } )+f'(\cos { x } ) $$, then $$g(x)$$ is decreasing in

$$f(x)=e^{3x}-sinx+x^{2}$$, Find $$f '(x)$$

Given that f(x) is a differentiable function of x and that $$f(x).f(y)=f(x)-4-f(y)+f(xy)-2$$ and that $$f(2)=5$$. Then $$f'(3)$$ is equal to

The curve that passes through the point $$(2,3)$$ and has the property that the segment of any tangent to it lying between the coordinate axes is bisected by the point of contact, is given by

If the line $$y=4x-5$$ touches to the curve $${ y }^{ 2 }=a{ x }^{ 3 }+b$$ at the point $$(2,3)$$ then $$7a+2b=$$

If $$f(x)$$ is an even function, where $$f(x)\ne 0$$, then which one of the following is correct?

For the curve $$x=t^2-1$$, $$y=t^2-t$$, the tangent is perpendicular to $$x$$-axis then

Let $$f\left( x \right) = {\tan ^{ - 1}}x - \frac{{In\left| x \right|}}{2},x \ne 0.$$. Then $$f\left( x \right)$$ is increasing in

If the tangent at $$({x_1},{y_1})$$ to the curve $${x^3} + {y^3} = {a^3}$$ meets the curve again at $$({x_2},{y_2})$$, then

If the error committed in measuring the radius of the circle is $$0.05\%$$, then the corresponding error in calculating the area is: