If $x = A \cos 4t + B \sin 4t$,then $\frac{d^2x}{dt^2} = $

Suppose the function $f(x) - f(2x)$ has the derivative $5$ at $x = 1$ and derivative $7$ at $x = 2$. The derivative of the function $f(x) - f(4x)$ at $x = 1$ has the value equal to:

Let $P(x)$ be a polynomial of degree $2$,with $P(2)=-1, P^{\prime}(2)=0, P^{\prime \prime}(2)=2$. Then $P(1.001)$ is

$f(x)$ is a twice differentiable function such that $f^{\prime \prime}(x)=-f(x)$ and $f^{\prime}(x)=g(x)$. If $h(x)=(f(x))^2+(g(x))^2$ and $h(1)=2$, then $h(2)=$

The second order derivative of $\cos^{-1}(4x^3 - 3x)$ with respect to $\cos^{-1}(2x^2 - 1)$, where $\frac{1}{2} < x < 1$ is

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :