(1 point) Find $h^{\prime}(1)$ if $h=f \circ g . f(x)=7 x^{2}-1$ and the equation of the tangent line of $g$ at 1 is $y=8 x+6$. Preview My Answers Submit Answers

Step 1 ：Find the derivative of function \(f(x) = 7x^2 - 1\), which is \(f'(x) = 14x\)

Step 2 ：Given that the derivative of function \(g\) at \(x=1\) is 8, so \(g'(1) = 8\)

Step 3 ：The derivative of the composition of two functions is given by the chain rule, which is \((f \circ g)'(x) = f'(g(x)) \cdot g'(x)\)

Step 4 ：Therefore, \(h'(1) = f'(g(1)) \cdot g'(1) = 14g(1) \cdot 8\)

Step 5 ：The equation of the tangent line to \(g\) at \(x=1\) is \(y=8x+6\), so \(g(1) = 8(1) + 6 = 14\)

Step 6 ：Substitute \(g(1) = 14\) into the expression for \(h'(1)\), we get \(h'(1) = 14(14) \cdot 8 = 1568\)

Step 7 ：\(\boxed{h'(1) = 1568}\)